Multiplayer online battle arena (MOBA), also known as action real-time strategy (ARTS), is a sub-genre of the real-time strategy (RTS) genre[citation needed], in which often two teams of players compete with each other in discrete games, with each player controlling a single character through an RTS-style interface. It differs from traditional RTS games in that there is no unit construction and players control just one character. In this sense, it is a fusion of action games and real-time strategy games. The genre emphasizes cooperative team-play; players select and control one "hero", a powerful unit with various abilities and advantages to form a team's overall strategy. The objective is to destroy the opponents' main structure with the assistance of periodically spawned computer-controlled units that march towards the enemy's main structure via paths referred to as "lanes".
More: http://en.wikipedia.org/wiki/Multiplayer_online_battle_arena

VS

A massively multiplayer online game (also called MMO and MMOG) is a multiplayer video game which is capable of supporting hundreds or thousands of players simultaneously. By necessity, they are played on the Internet. Many games have at least one persistent world, however others just have large numbers of players competing at once in one form or another without any lasting effect to the world at all. These games can be played on any platform it, be it the personal computer, a game console such as the internet capable PSP, PlayStation 3, Xbox 360, Nintendo DS, PS Vita or Wii, or mobile devices and smartphones based on such operating systems as Android, iOS and Windows Phone.
More: http://en.wikipedia.org/wiki/Massively_multiplayer_online_game