What is the difference between reversing and inversing moves?
One of them (inverting) has a generally understood meaning while the other one (reversing) does not.
Inverting means you do two things: read the move sequence from right to left, and also reverse all the move directions (clockwise becomes anticlockwise and vice versa).
Reversing can mean any of these:
1. Same thing as inverting. Probably the most common usage, since "inverse" (in the mathematical sense) is not in the common lexicon.
2. Reading the move sequence right to left, but without reversing the move directions. E.g. R U R' U R U2 R' becomes R' U2 R U R' U R.
3. Reading the move sequence left to right, but reversing the move directions. (I had never seen this until now but I guess it's an option.)
Sense 2 is sometimes useful for RU 2-gen algs; it captures what happens when you both invert
and mirror the alg. Under some weak assumptions, an alg that's regripless from home grip will have a mirror-inverse that's also regripless from home grip.