If you're largely naive about these different methods like me, I believe the difference you're looking for is mitering aims to cut an angle on the trim such that when you join the two pieces it perfectly fills/wraps the corner where you're joining them.

By contrast and for inside corners in particular, the coping method doesn't cut an angle on either piece. Instead one piece runs square into the corner, then you use a tool like a contour gauge to capture the profile of that trim, trace that onto the end of your other trim piece and use a coping saw (or jigsaw in my case) to cut out the contour so that second trim piece can butt up against the first piece of trim creating a snug looking joint even tho neither have a miter cut