They all look the same in the end, so you may be confused why there are so many different types of drywall - or oblivious. Never mind that, there are so many different things to call it: sheetrock, wallboard, gypsum wallboard (or its shorter cousins gypsum board and gyp board, and the Notorious GWB). And sometimes they change “board” to “panel”. Those are all the same thing, and some of the variations on it include:
Gypsum rock is mined, crushed, baked, mixed with water to make a slurry, poured out between 2 sheets of paper, dried, cut, then shipped to the jobsite. Thus the nickname sheetrock as it literally is rock spread out on a sheet of paper. It is usually ½” thick for residential jobs and 5/8” thick for commercial jobs (which creates a flatter wall surface and offers more sound and/or fire resistance), but also comes in ¼” and 3/8” thicknesses.
It can be curved – thinner panels bend tighter as shown in this flyer by the Gypsum Association – and wetting it or scoring it allows tighter radii (so sometimes moisture-resistant board is used).
The narrow ends of the drywall panels are tapered slightly so that when you apply the plaster (“mud” and paper tape to cover the joints, that added thickness ends up approximately flush with the main part of the panel. Don’t ask me why they don’t taper the long sides, too, but that is a clue as to why the recommended practice is to install the panels horizontally on a wall rather than vertically – the staggered horizontal joints are less visible when you look down along the wall, whereas a continuous tall vertical joint will have a very shallow “speed bump” of plaster every four feet. So drywall walls are not flat but they are much flatter than their predecessor, plaster and lathe. (Flatness and horizontality aren't the same thing, as if you cared).
A few of the major types of drywall include: