My (limited) experience is that warping that happens from tension being released happens fast. On a table saw it can cause sudden kickback as the wood suddenly distorts and binds. Cupping that occurs from uneven moisture does not (again, in my limited experience) happen so fast. I have resawn pieces that looked fine only to find an hour, or a day, later they were cupped. The cupping that occurs from uneven moisture can sometimes be corrected to some extent by moistening the dry concave side and drying the moist convex side. This is a trick sometimes used for warped plywood sheets, especially if the warp is in just one direction. It works less well if the plywood is all twisty, as often happens with thin pieces. A simple approach to the plywood is to just place it concave side down on grass with the convex side facing the sun. Maybe some moisture sprayed on the concave side will help before laying it down. There are a number of variations on this theme for plywood. One danger is it can be so effective that the board quickly warps the other way, especially if it is thin plywood!
I have also tried this with some success for thin pieces of solid resawn wood that had cupped I have sprayed the concave side with water and placed that side down on my bench (on some plastic to protect the bench) and then directed some heat at the convex side. I have some of those ceiling mounted radiant heaters that worked okay for this. Again, if the pieces are thin the cupping can quickly go the other way. Ooops! And if the added moisture or heat is uneven other distortions can happen. I have not tried this for pieces longer than a foot or two. That might be harder since it is harder to heat a large piece evenly.
I have no idea how often this works for solid wood or whether it is likely to work well for somewhat thicker or longer pieces. I had enough success to figure it was at least worth mentioning.