Doom Clone is what FPS was called before the term FPS was coined. See also Diablo Clone.
Souls Like is not a Hack-n-Slash, that's a simpler arcade genre. think Gauntlet or Golden Axe.
Immersive Sims, aka 0451 games, are highly interactive games inspired by the likes of Thief, System Shock, and Deus Ex. Basically they rely on many small game systems interacting together rather than pre-scripted events.