I love you for asking why it isn't a MMO when you don't know the difference
Both Diablo 1 and 2 are online multiplayer games but are not MMO's. MMO's have persistent worlds and have hundreds to thousands (or more) players in a 'room' at the same time. Think World of Warcraft for MMO, 1000's of players can interact in-game anytime they bump into each other vs. Starcraft for online game, thousands (or more) play the game BUT only 8 (iirc?) people can play a game in a 'room' at once.
If you've ever played a game on Battle.net you'd understand how to join / whatnot, it is very easy and I still regard it as one of the best (if not the-best) room-based match making systems out there (With the stupid friend code / random with anyone Wii system being the worst... Oh Wii you let me down so magnificently). Diablo 1 and 2 had very similiar multiplayer experiences, both were on battle.net (Free to play), and both were room-based. For D1 the max players per game was 4 while in D2 it was 8 (Apparently D3 is being made to suit about 3-5 players in the game? I'm sure you'll be able to have at least 8 though). You could only join games of nightmare and hell difficulty if you had finished normal and nightmare difficulty respectively on that character, other than that you could find rooms to play in, or if you knew the name of a game you wanted you could type it in and enter (might have needed the password) and join as long as it wasn't full.
Multiplayer for these games was a lot like singleplayer:
Diablo 1 was pretty much the same except you couldn't do a few quests (and I think your single player could go over to multiplayer at any time) but the problem with the multiplayer was that character information was stored on your computer (leading to plenty of hackers [invisible ghosts, 1HKO heal other, invincibility, etc]) and duping (Cloning items) was so easy to do it wasn't funny.
Diablo 2 vastly improved the multiplayer by having a closed b.net setting (The character information was stored on the blizzard servers) making it harder to use cheats (even though maphack became almost omnipresent, and there was gambling hacks to see if an item was unique / rare for a while). Duping was also significantly harder to do (and when methods became known to the general population a patch was introduced and 'ruststorm' was activated [took duped items and made them garbage]).
Diablo 3 will apparently be on battle.net (or an improved version?). I'm guessing much of it will be similiar but since they say that they are adding other features I'd speculate that they'd add a trading system outside of games, probably a filter for choosing which game you want to join (Like Warcraft 3's custom games), and potentially a way to invite friends into a game you've made.






