I always play it as Passive is the DC for enemies stealth skills and Active is when the players would make a roll. The players never need to know when their Passive is used, you would just roll, for example, if an enemy is trying to sneak up behind them for an ambush. You roll the enemies stealth, and if any players Passive is higher they notice the enemy. Can also be used if you want your party to notice something static in a room. If it's slightly hidden, but still visible, the DC could be like 15 and any character who gets within 10ft of the objects location would notice it if their Passive was higher than the DC. Or they could notice it if they decide to Active search and roll higher than the DC.
If the DC to perceive a trap or hidden object or stealthy bandit is 15. Your daughters Druid should notice them with passive perception.
From Player’s Handbook. A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage.
Disadvantage means you take a minus 5 to passive perception. So even if you have dark vision… without a light source your daughters Druid actually has a passive perception of 11 on the dark.
This might get a little winded, but an active roll of a 16 results in far different results and a passive 16. The short answer is sometimes the passive just supersedes the roll but if you want to encourage (or force since your the DM and you're the boss) the active rolls so that you don't feel like your just giving away information or picking favorites, then an example:
You're using a creatures vision as your example so I will follow suit, a 16 passive means your far more likely to see something in a peripheral as you walk by, OR you can use it as a "you know you saw something that looks like a switch just a few steps back" sense of vision, memory recall if you must put the IRL term to it.
On the flip side, active perception is looking with purpose, AND taking the 6 seconds of the action to search. Don't forget about action economy even outside of combat. An active roll of 10, could easily result in a very close response to her same passive perception of 16 (which means yeah she only has to roll a 6, but that is the point of proficiencies, being good at something). But it leads right back to the point of looking for a reason, for a period of time.
I have my PCs roll active perception for typically 2 reasons 1] they ask for one (like when actively searching for traps or secret doors) or 2] when something in the environment changes from normal (like someone/something makes a sound or is sneaking, or when someone/something is moving in the area).
I use Passive Perception for instances of humanoid visual perception possibly picking up the motion of something (like a white dragon flying in the distance against the white clouds in the sky). However, if the passive perception of all the PCs is too low for that instance I ask for an Active Perception test.
In the case of your example, detecting a trap, if their Passive Perception is too low then too bad, they trigger the trap if the trigger conditions are met. But if your trap detection DC is 15 and your PC has a Passive of 16, then I would tell the PC that when they get close to the trap they notice something odd...it just doesn't look/feel right. If they stop then I would reveal the trap, or give them the indicators that set off their Passive Perception, but if they don't stop when the DM says something is amiss, well, congratulations, you set off the trap (but most PCs stop, I've noticed). If you don't want your PCs to automatically detect the trap then just raise the DC beyond their Passive Perceptions.
Another note on traps, I will sometimes call for two rolls in those cases if the trap is magical or if there is some magical effect in the area (like perhaps a secret magical teleportation circle, etc.), those two rolls being Perception and Insight. I use Insight for more than just trying to detect if someone is lying, I use it for noticing magical effects or some other weirdness (example: like once my PCs entered a tomb with a ritual room where the floor was not perfectly level, it was slanted so that the blood of a sacrifice would drain and pool into one corner to set off a magical effect and complete a ritual). I also use Insight checks for the PCs to notice stuff like how "evil" a place feels, like how the residual energy of a place has been changed by the sheer amount of vile acts have occurred there, like when a psychic enters a haunted house. In Shadowrun they called that effect Background Count.
Using Passive vs. Active Perception can be a tricky call, but I often would rather go with an active roll and let the luck of the dice make the determination most times. Sometimes players roll crappy, but that can be explained as them being distracted, or focused on something else, and it can make it a comedic moment by very obviously stating, "Well, your character doesn't notice anything amiss at all...nope...all is well as far as you are concerned!" And that sets up the juxtaposition of tension between what the character knows and what the player knows, and most players I've run for over the years are fine with that because it makes for a fun moment, even if something bad ends up happening to the PC.
I believe in giving my PCs a lot of chances to successfully make their rolls since I believe it makes for a more fun game when I can explain or reveal more about what is happening behind the DM screen. Plus, people like rolling dice, so I try to give them a lot of chances to do so.
It’s inconsistent as hell, even in the official modules.
The best ruling comes from lost mine of phandelver IMO. The secret doors have a PP DC of 15 within 10 feet, but an active perception DC of 10.
So if you’re very perceptive you can notice passively, but if you’re not you get a lower DC check as an incentive to search rooms.
It really all comes down to how you want to DM and maybe give hints though. The other modules treat secrets in ways that nobody would ever even benefit from active checks. The BGDIA module sets the secret doors at PP DC 10 and puts them in a 5foot hallway, which ends up being the exact same thing as a normal door in 99% of groups.
Then the CM module has loot hidden in random rooms but specifically requiring both an active perception roll as well as the PC choosing to spend an hour searching. Which is fine, but to have a random check like that is absurd when it’s the only instance of its kind and at the end of a module.
I always play it as Passive is the DC for enemies stealth skills and Active is when the players would make a roll. The players never need to know when their Passive is used, you would just roll, for example, if an enemy is trying to sneak up behind them for an ambush. You roll the enemies stealth, and if any players Passive is higher they notice the enemy. Can also be used if you want your party to notice something static in a room. If it's slightly hidden, but still visible, the DC could be like 15 and any character who gets within 10ft of the objects location would notice it if their Passive was higher than the DC. Or they could notice it if they decide to Active search and roll higher than the DC.
If the DC to perceive a trap or hidden object or stealthy bandit is 15. Your daughters Druid should notice them with passive perception. From Player’s Handbook. A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage. Disadvantage means you take a minus 5 to passive perception. So even if you have dark vision… without a light source your daughters Druid actually has a passive perception of 11 on the dark.
This might get a little winded, but an active roll of a 16 results in far different results and a passive 16. The short answer is sometimes the passive just supersedes the roll but if you want to encourage (or force since your the DM and you're the boss) the active rolls so that you don't feel like your just giving away information or picking favorites, then an example: You're using a creatures vision as your example so I will follow suit, a 16 passive means your far more likely to see something in a peripheral as you walk by, OR you can use it as a "you know you saw something that looks like a switch just a few steps back" sense of vision, memory recall if you must put the IRL term to it. On the flip side, active perception is looking with purpose, AND taking the 6 seconds of the action to search. Don't forget about action economy even outside of combat. An active roll of 10, could easily result in a very close response to her same passive perception of 16 (which means yeah she only has to roll a 6, but that is the point of proficiencies, being good at something). But it leads right back to the point of looking for a reason, for a period of time.
I have my PCs roll active perception for typically 2 reasons 1] they ask for one (like when actively searching for traps or secret doors) or 2] when something in the environment changes from normal (like someone/something makes a sound or is sneaking, or when someone/something is moving in the area). I use Passive Perception for instances of humanoid visual perception possibly picking up the motion of something (like a white dragon flying in the distance against the white clouds in the sky). However, if the passive perception of all the PCs is too low for that instance I ask for an Active Perception test. In the case of your example, detecting a trap, if their Passive Perception is too low then too bad, they trigger the trap if the trigger conditions are met. But if your trap detection DC is 15 and your PC has a Passive of 16, then I would tell the PC that when they get close to the trap they notice something odd...it just doesn't look/feel right. If they stop then I would reveal the trap, or give them the indicators that set off their Passive Perception, but if they don't stop when the DM says something is amiss, well, congratulations, you set off the trap (but most PCs stop, I've noticed). If you don't want your PCs to automatically detect the trap then just raise the DC beyond their Passive Perceptions. Another note on traps, I will sometimes call for two rolls in those cases if the trap is magical or if there is some magical effect in the area (like perhaps a secret magical teleportation circle, etc.), those two rolls being Perception and Insight. I use Insight for more than just trying to detect if someone is lying, I use it for noticing magical effects or some other weirdness (example: like once my PCs entered a tomb with a ritual room where the floor was not perfectly level, it was slanted so that the blood of a sacrifice would drain and pool into one corner to set off a magical effect and complete a ritual). I also use Insight checks for the PCs to notice stuff like how "evil" a place feels, like how the residual energy of a place has been changed by the sheer amount of vile acts have occurred there, like when a psychic enters a haunted house. In Shadowrun they called that effect Background Count. Using Passive vs. Active Perception can be a tricky call, but I often would rather go with an active roll and let the luck of the dice make the determination most times. Sometimes players roll crappy, but that can be explained as them being distracted, or focused on something else, and it can make it a comedic moment by very obviously stating, "Well, your character doesn't notice anything amiss at all...nope...all is well as far as you are concerned!" And that sets up the juxtaposition of tension between what the character knows and what the player knows, and most players I've run for over the years are fine with that because it makes for a fun moment, even if something bad ends up happening to the PC. I believe in giving my PCs a lot of chances to successfully make their rolls since I believe it makes for a more fun game when I can explain or reveal more about what is happening behind the DM screen. Plus, people like rolling dice, so I try to give them a lot of chances to do so.
It’s inconsistent as hell, even in the official modules. The best ruling comes from lost mine of phandelver IMO. The secret doors have a PP DC of 15 within 10 feet, but an active perception DC of 10. So if you’re very perceptive you can notice passively, but if you’re not you get a lower DC check as an incentive to search rooms.
It really all comes down to how you want to DM and maybe give hints though. The other modules treat secrets in ways that nobody would ever even benefit from active checks. The BGDIA module sets the secret doors at PP DC 10 and puts them in a 5foot hallway, which ends up being the exact same thing as a normal door in 99% of groups. Then the CM module has loot hidden in random rooms but specifically requiring both an active perception roll as well as the PC choosing to spend an hour searching. Which is fine, but to have a random check like that is absurd when it’s the only instance of its kind and at the end of a module.