crpg is a computer rpg.
the other kind is pen and paper.
crpg's generally have a fixed plot and modules, though they can range from having none to lots of replay value depending on the number of side quests/multiple endings.
and then theres mmorpgs, massively multiplayer online rpgs, like UO, evercrack, and daoc. some, like uo and daoc, have minimal plot (or none) affecting the players (though i think UO now has a plot). (UO, as far as i'm concerned, is the most rpg-ish crpg ever, in that you can do all sorts of things, your skills aren't set at character creation, that sort of thing. daoc, all their is is fighting. star wars galaxies should be very good, i think).
then theres squaresoft rpgs, which recently have become little more than interactive movies. the best of those, IMHO, was final fantasy 4 (2 in the US), which had the most plot twists of them all (though its not anything like the interactive movie that the PS versions have been.)