Gaining insight into what a puzzle piece actually is
Recognition is the ability to look at a puzzle piece and understand where you've seen it before or gain insight into its purpose. It's the transition from an unknown to a known aspect.
This may be the moment those random squiggles on the wall look like an alphabet, or noticing that the raised bumps on the floor might be braille. Or it may be playing with an unknown device then realising it's an olive pitter. It could also be recognizing an action, such as noticing that the people in a photo are holding out different numbers of fingers.
Recognition is different than association, though they tend to support each other. It's possible to associate pieces with each other even if you aren't sure what they are. Recognition tends to focus on individual pieces — knowing in isolation what the purpose of one piece is. This recognition may then be used to associate pieces with each other.
All recognition requires that the player has been educated. They cannot know the aspect of a piece if that knowledge is not part of their experience. For example, if you've never seen an exhaust manifold it will be difficult to recognize one.
If the player needs knowledge which is not found within the game, it's called external knowledge. This can be problematic for recognition puzzles, as it's hard to establish what is the common experience players have. We assume the player can recognize a painting, or a book, for example, but not that they'll recognize the exhaust manifold.
Recognition can happen in layers. Using the same example, a mechanic may recognize the exhaust manifold of a 2015 Toyota Camry, whereas his friend may only recognize it's part of a car, and yet his other friend may not recongize anything beyond a set of connected pipes. Either the puzzle has to be designed to the generic understanding (connected pipes), or the game must provide enough information to make a more detailed identification.
For many objects it can be challenging to decide what is common knowledge. Many experienced players will recongize morse code, braille, the pigpen cipher, and roman numerals, but many players will not. It's important to consider what an inexperience player would recognize.
If players have access to external information then external knowledge need not be taboo. There are plenty of detective games where research is part of the puzzle. Or if the player is instructed to make use of their phone, perhaps searching specific knowledge is expected.
It's also possible to design pieces where full recognition isn't required. To use the exhaust manifold again, a game may have several pipes that need to be connected. A player may identify the manifold as the missing piece. They have reconigized its in-game purpose without connection to the external world.
Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.