Drywall, drywall, et, are both names for gypsum board.
In a nutshell, there are essentially four types of gypsum board. The basic board, with a gray paper facing, is the most common. The greenboard that you mentioned is "MR" or moisture resistant. MR means you use it in high-humidity areas, or areas where light water may be a factor. It really shouldn't be used in wet areas like a tub surround or shower stall. If used on ceilings, greenboard must be screwed to framing not more than 12" oc. The additives used to make it MR also reduce its stiffness, making it more susceptible to sagging. The third is "blueboard" and blueboard is used for veneer-coat (1/8th inch thick or so) plaster. The last is fire board, or "X" board. It's 5/8ths inch thick and has a gray paper facing.
In wet areas like a tub surround or shower, don't use a gypsum prooducct. Use half-inch cement board (Wonderboard, Durock, or Hardie board) as a backer for the shower/tub tile.