I'd argue that the next room case is dominated by considerations of future real interactions, so mostly isn't acausal.
I think I'd prefer calling it "acausal trade vs. pre-causal acausal trade" because it seems that the underlying phenomenon is exactly the same in both cases, it's the circumstances surrounding that are different. But this is just a minor terminological quibble.
Acausal trade happens when two agents manage to reach a deal with each other, despite not being able to interact causally (and, in some cases, not being sure the other one exists). Consider, for example, the prisoner's dilemma played against another copy of yourself, either in the next room or the next universe.
But those two situations are subtly different. If my copy is in the next room, then we will interact after we've reached our decision; if they're in the next universe, then we won't.
It might seem like a small difference, but my simple way of breaking acausal trade succeeds in the "next universe" situation, but fails in the "next room" situation.
So it would be good to distinguish the two cases. Since the terminology is well established, I'll call the "next universe" situation - where there are no interactions between the futures of the agents - to be "fully" acausal trade.