What do you use to determine which is which, gut feeling, or some set of criteria?
I use what I would call a mix of criteria and gut feeling, which is probably best to use concrete examples in order to cover.
For the scenario, let us assume that I have described a study to the players that their characters have just entered. There are all sorts of things typical to a study (desk, bookshelves, chairs, a couch, a small table, light sources, and numerous books, papers, writing supplies and nick-nacks, etc.
Let us also assume that there is something hidden that the character is looking for, which is currently located in the lower drawer of the desk (unknown to the player and their character).
If the player declares that their character is opening the desk drawers to look for this item, there is no roll - the effort is successful because I'm certain the character will see the item that they have placed right in front of their eyes by opening the drawer.
If the player declares that their character is going to stand near the middle of the room and glance around to look for this item, there is no roll - the effort can't possibly succeed because they can't see through the desk and into the closed drawer.
If the player declares something less specific, for example that the character checks things which seem like good hiding places, I'm not certain that includes opening the drawers so there would be a check to resolve that uncertainty - and I would likely use a passive check in that case because the task is one that can be done repeatedly and I'd rather not go through the motions of roll > "You don't find it" > "I keep looking." > repeat. If the character can't succeed with the passive check, then that just means the player needs to think of a new strategy for the task at hand to either gain advantage, or make their success certain.
The only times that a search action gets resolved with an actual die roll at my table seems to be when there are a specific limited amount of time in which to find something (i.e. if the character in the above scenario doesn't find the item hidden in the study within the first minute of their search, they will be caught looking by the owner of the study), or when the actions are being resolved in combat turns and there is still uncertainty).
The same style of process is applied regardless of what use of an ability score is in question, not just for finding hidden objects - but going in-depth with each would be quite more words than I feel is appropriate for a single post.