Not to be confused with Ditto the Pokémon.
A ditto match or a mirror match (often shortened to just ditto or mirror), is a match where both players choose the same character. They are different from other matches in that neither player has an objective matchup or stage advantage over the other player. The name comes from the definition of 'ditto', which means 'the same'. While possibly just a coincidence, Ditto is also the name of a Pokémon that frequently appears in the Smash series, whose gimmick is the ability to copy their opponents' appearance and moveset. Ditto matches occur frequently during tournaments, often between top-tiered characters, as they are the most commonly played.
Strategies
Strategies for a ditto often vary greatly from the character's normal strategy. Since both players are using the same fighter against each other, both likely know what strageties the other will use ahead of time. This requires the players to take a different approach when playing. An example would be a Melee Jigglypuff ditto; both players have access to Jigglypuff's strong aerial drift and large, disjointed hitboxes, and neither can be comboed very easily due to Jigglypuff's floatiness. If one player attempts to land Rest to close stocks out early, the other can easily retaliate with their own and force the game back to a neutral position at worst. Due to this, Jigglypuff dittos disproportionately revolve around the neutral game, with the player that has superior patience and spacing usually edging out their opponent. Another example would be in a Super Smash Bros. Captain Falcon ditto match; due to Captain Falcon's incredible combo ability along with his own vulnerability to combos, the match ends up taking advantage of player flaws more frequently than usual.
A general strategy is to be unpredictable at all times and use experience with a character (knowing combos or recovery strategies) against the other player. Snake is a good example of this; in a mirror match of the two, the players have to use projectiles in such ways to make the stage difficult to navigate for the other player.
Matchups
Ditto matches should theoretically always be perfectly even matchups, since they are literally using the exact same fighter. These circumstances should allow a 50/50 chance of winning between two evenly-skilled players. However, due to gameplay mechanics like port priority, this is not always precisely the case. The most obvious imbalance regards simultaneous KOs and is overridden in tournaments by the "Suicide Rule". The remaining differences generally have little effect on practical tournament gameplay, though for some characters like Snake the imbalance can be noticeable.