A cheat is any method, legitimate or not, that gives you an advantage not normally there in a game. Most cheats are placed in a game by the developer, but you can also use a cheat device to make minor “hacks”.
Cheats and “secrets” are not all that different, and you can often find that these features make things more challenging rather than easier (such as Saikyō mode from Street Fighter Alpha 3).
One of the primary “cheats” in fighting games are secret moves, which unlike most secret characters, are usually actually completely undocumented when a game is released. Usually, these are considered okay cheats to use in serious play. There are also unintentional cheats that use bugs (e.g., there are “air supers” in KOF ’94 and KOF ’95 were actually only meant to be used on the ground). Whether these are okay depends on the game, and often depends on who you’re playing against.
Secret moves are intentionally put there by the developers, so they are safe to play around with. Bugs run the risk of freezing the whole system, or otherwise making it impossible for either person to fight (such as one person getting stuck inside the other, or being trapped in some weird midair knockdown, and so forth), so you must be careful if you are trying to use them.