There's a few definitions floating around, but in this case:

Roguelike, with a k: Progress resets completely between runs.

Roguelite, with a t: Some progress carries over between runs, i.e. you can unlock "account"-wide bonuses that you can use to make yourself stronger in the next run.

Though GT might not even be considered a roguelite by some standards, because its runs aren't procedurally generated - it's the same map and same events every time. That's getting into the nitty-gritty of game categorization, though.