At its simplest, MMORPG stands for Massive Multi-player Online Role Playing Game while MMO stands for Massive Multi-player Online.
This may sound the same, but there are subtle differences, since all MMORPGs are MMOs but not all MMOs are MMORPGs. An RPG is a game where the player assumes the role of a character in a virtual/fictional setting. But, even though you always assume the role of a character in an MMO, certain MMOs (like Audition for example) are not to be considered to be MMORPGs.
Audition is an MMO where you represent yourself in avatar form. You compete against other characters in dance-offs and compete to be the best dancer. You also get currency to buy your avatar clothes and hairstyles. Despite this, Audition wouldn’t be considered an MMORPG because the game doesn’t really take place in a fictional setting – it’s aim is to look like a real world environment.
Now, World of Warcraft by Blizzard is a great example of an MMORPG. In this, you are the main character and fight and build to gain resources. You think of strategies and look for the best time to conquer new territories. You can fight with other people in a party to work together and kill your enemies, or you can fight against each other in the player versus player arena. This would be considered an MMORPG because not only do you assume the role of a fictional character, you also are in a fantasy-based land.
All MMOs will have chat rooms, or some sort of chat system so you can communicate with other people. If a game does not offer the possibility to communicate with other players, it cannot be considered an MMO. The social aspect here is key.
There are more genres to MMOs then just RPGs, though such as: simulation (Sims Online), real time strategy (Sparta: War of Empires or Warcraft), puzzle (Puzzle Pirates), and much, much more.
The layout of MMORPGs are also different from each other. Some MMORPGs, like Sparta: War of Empires and Stormfall: Age of War, have you start out right in the fantasy land it takes place in. Others, like Grand Chase, have you start out on a world map and makes you join a room with other four players, but Grand Chase is one of those games that is very hard to tell if it’s an MMORPG or MMO, since the game takes place in a real life setting yet others might say that it is a fictional place in a fantasy land. If it takes place in a fantasy land, it’s typically an MMORPG.
There are some games that are difficult to categorize as strictly an MMO or MMORPG, although the major games in these categories usually are both.