Thieves & Kings
In 5th Edition D&D there is a definitive difference between Perception and Investigation, both using different statistics as their basis, and thus being useful under different circumstances.
Perception : Wisdom (Perception) checks let you spot, hear, or otherwise detect the presence of something. It measures your general awareness of your surroundings and the keenness of your senses. For example, you might try to hear a conversation through a closed door, eavesdrop under an open window, or hear monsters moving stealthily in the forest. Or you might try to spot things that are obscured or easy to miss, whether they are orcs lying in ambush on a road, thugs hiding in the shadows of an alley, or candlelight under a closed secret door.
Investigation : When you look around for clues and make deductions based on those clues, you make an Intelligence (Investigation) check. You might deduce the location of a hidden object, discern from the appearance of a wound what kind of weapon dealt it, or determine the weakest point in a tunnel that could cause it to collapse. Poring through ancient scrolls in search of a hidden fragment of knowledge might also call for an Intelligence (Investigation) check.
So. What we learn from this is, that looking for a hidden trap, or a potential ambush requires Wisdom (Perception), while finding the most likely location of a hidden amulet in a guard’s room, or the trigger mechanism for a known trap uses Intelligence (Investigation), and are two separate activities and use two separate skills.
Here are a few examples:
Secret Door : “Secret doors are made of stone and blend in with the surrounding walls. Spotting a secret door from a distance of no more than 10 feet without actively searching for it requires a passive Wisdom (Perception) score of 15 or higher, whereas a character who takes the time to search the wall can find the secret door with a successful DC 10 Wisdom (Perception) check.”
Snare Trap : “If the characters are searching for traps, the character in the lead spots the trap automatically if his or her passive Wisdom (Perception) score is 12 or higher. Otherwise, the character must succeed on a DC 12 Wisdom (Perception) check to notice the trap.”
Weakened Bridge : “A character next to the bridge can discern that the construction is faulty with a successful DC 15 Intelligence (Investigation) check.”
We should assume that the Player Characters are competent. That when they move they are always searching for enemies and that they are moving along taking precautions against hallway traps and ambushes. While the rules seem to indicate that every time the characters move they have to declare they are searching, or they only receive their Passive Perception (PP) score (and sometimes not even that at all), I’m not generally fond of “hoop-jumping”, especially in a heroic adventure game. Generally, I am only going to require players to state that they search chests, passageways and doors for traps, and allow the player’s Passive Perceptions apply to most situations.
it can also be assumed that during wilderness travel, everyone is being careful, and “slow” travel under the rules; 20’-per round, or 20 miles per day, is considered typical, with adventurers carefully checking suspicious locations, doing some basic tracking and keeping an eye out along the trail or passages ahead and behind themselves. Under these circumstances Wisdom (Perception) checks are going to be called for, should an unusual thing be noticed which requires a specific check to be asked for. If Slow travel is not being taken, then checks with disadvantage should be required to spot ambush locations or suspicious roper stalactite formations along the dungeon passage.
It should further be mentioned, that looking in the proper location for something does not require a Wisdom (Perception) roll to actually see it. The mountains are always on the horizon, a ridge near a crossroads is a notable landmark, and a signpost is meant to be obvious to travellers. Note, however, that one must still describe where you are looking for he skill to succeed. If you are looking for a key hidden in a room, you must describe where you are searching before the roll can be made. Too often, adventurers simply state “We search the room for clues…”, and expect to find an immediate result. If you say “We look around the room”, it also implies you are searching the walls and floor for secret doors, not rummaging through the chests of clothing for a hidden cavity or forgotten pouch of coins. This might be a little nit-picky, but I want to impress upon adventurers a less “lazy” approach, and actively think how they intend to find things as adventurers and role-players.
However, looking for a reputed hidden hatch in the ruins of a fallen tower is going to require a different form of identification; the Intelligence (Investigation) check. These checks do not have a passive value. If you have to search a library for a specific book, search the rubble of a ruin for a lost hatch, or discover the meaning behind an arcane passage found in a book, then this is the skill to use. It grants information that goes beyond merely peering at an object, rather granting knowledge about one’s environment that is optional to the encounter, or simply not straightforward. Intelligence itself is about accumulated knowledge, the capacity to adapt and learn, not just innately perceive something. It applies intuitive thinking, rather than good hunches.
Therefore, it is often a secondary skill requiring time to sort given facts, and generally cannot occur during combat or under duress. It also implies explaining to the DM what you intend to do with the skill. Wandering through a tunnel will not innately grant an Intelligence (Investigation) check to determine its safety; that requires thoughtful examination of the tunnel and its supports. I will assume they are being careful and approach dangerous locations with some degree of caution, but they still need to think about the situation and apply themselves to determine what might be dangerous.