dungeon mimics can be sorted into three distinct categories:
Consume-And-Replace mimics do as the name implies - whatever they mimic they do so by consuming a pre-existing one and copying its former appearance near-exactly.
Hermit mimics are so called based on hermit crabs - they hide in something normal, and use it as camouflage.
Classical mimics are the most well known - they're simply born, hatched, formed, etc already looking like something else, or metamorphose into that form at a set point in their lifespan.
for a rather interesting example of a C&R mimic, let's look at your Common Wall Mimic.
This actually refers to a rather small genus of slimes that have adapted to be able to consume and absorb common wall materials, such as the stone bricks of your average catacomb, and take their place both appearance-wise and structurally. As such, sometimes you're better off avoiding them entirely rather than slaying them, as they may have taken the place of a load-bearing wall.
While these may be hard to spot if you don't know what to look for, there's a few signs you may be looking at a common wall mimic: a slimy residue on and around a section of wall with no obvious source, a total lack of vegetation on a section of wall in an area that has vegetation present elsewhere, and even slight undulations or perturbations of the suspicious wall section - that's actually the slime breathing, and yes, they breathe. You'd be surprised to know how many adventurers don't realize slimes have to breathe.