Roguelike - A top-down tile-based turn-based role playing game with procedurally generated levels which feature a fail state in which all progress is lost, typically designed to reward learning and experimenting with the provided resources. (These games are like Rogue!)
Rogueish - A game in any genre featuring any type of gameplay which features randomized challenges and opportunities as well as a fail state in which all progress is lost, typically designed to reward more or less clever combinations of the provided resources. (These games don't play the same way as Rogue but they're structured in the same way)
Roguelite - A game in any genre featuring any type of gameplay which features randomized challenges and opportunities and sometimes pretends like it has a fail state, typically designed like any other game. (It's not really like Rogue at all except for one characteristic)