Previous research has divided balance into three main types: internal, external and positional.
Internal balance is achieved when either every option available to a player has equal power, or every option is strong in some circumstance relative to other options.
External balance is achieved when all players are provided equal opportunity to advance throughout the game as a result of the game design.
Positional balance is applied to game designs that mitigate positive feedback loops which otherwise allow players in the lead to increase their lead throughout the course of a game.
I stand by both internal and external balance as valid and useful categories. However, I believe that positional balance participates in a broader third category: Engagement Balance.
Engagement Balance is achieved when all players are equally engaged in a game from start to finish. Because positive feedback loops leave little to no chance for flagging players to maintain winning chances, engagement balance is often threatened. However, players are often engaged due to other design factors, and may become detached for yet others.
Other minor balance categories:
Skill Variance Balance is achieved when the skill and/or experience of all players is equalized. Often this is achieved by intentionally introducing inequalities in the external balance: many designs include this as an optional feature. In other cases, multiplayer designs often allow players to self equalize by abusing direct player interaction (targeting the strongest player).
Skillset Balance is achieved when the actions required of players involve a wide variety of cognitive activities. For instance, a game that requires the use of visual spatial, verbal-linguistic, logico-mathematical and inter-personal thinking would display a very high skillset balance.