They are all variations of the Semi-stiff Legged Deadlift. Giving something a whole new name just due to some fine point of variation is silly. For some reason we don't do that with bench press. I just call them Romanian Deadlifts because its easier to say than Semi-stiff legged deadlift and its way easier to write RDL.
The "American" Deadlift is gay anyway. That extra ass squeeze at lockout is pretty much useless and overrated. It's not really contracting against the weight so there's not much difference between squeezing your ass while deadlifting or doing the dishes. I suppose for an inexperienced lifter it could help for activating the glutes. No use for anyone else.