The What Is of MMORPG, MMORTS, MMOFPS.

Online games refer to video games that are played over some form of computer network, most commonly the Internet. The expansion of online gaming has reflected the overall expansion of computer networks from small local networks to the Internet and the growth of Internet access itself. Online games can range from simple text based games to games incorporating complex graphics and virtual worlds populated by many players simultaneously. Many online games have associated online communities, making online games a form of social activity beyond single player games.

First-person shooters.
During the 1990s, online games started to move from a wide variety of LAN protocols (such as IPX) and onto the Internet using the TCP/IP protocol. Doom popularized the concept of deathmatch, where multiple players battle each other head-to-head, as a new form of online game. Since Doom, most first-person shooter games contain online components to allow deathmatch/arena style play.

Massively multiplayer online games.
Massively multiplayer online games were made possible with the growth of broadband Internet access in many developed countries, using the Internet to allow hundreds of thousands of players to play the same game together. Many different styles of massively multiplayer games are available, such as:

MMORPG (Massively multiplayer online role-playing game)
MMORTS (Massively multiplayer online real-time strategy)
MMOFPS (Massively multiplayer online first-person shooter)