It's just a typo. Head into a TTRPG community and be prepared to see rogue mispelled as rouge a lot.

There's roguelikes and roguelites but they get conflated. The definition is kinda subjective but it's basically any game that shares characteristics with the game Rogue. Permadeath, random generation, simultaneous turn-based, tile-based movement and maybe a couple more. Roguelites are anything that uses these concepts but doesn't stick so much to the formula. At least that's my definition and nobody agrees.