You can indeed do a branch-and-bottleneck structure without state-tracking that influences later choices, but the more frequently your structure re-merges, the more valuable state-tracking/delayed-branching becomes. In a classic time cave with no merges at all, state-tracking is effectively useless: in something like Long Live the Queen which constantly re-merges to a central sequence of events, state-tracking becomes the entire game: if a game like that didn’t have heavy state-tracking, it would constantly make all of the player’s earlier choices irrelevant.
So the ideas are, if not precisely the same thing, strongly linked.
To clarify a little: Dan’s delayed-branching diagram is a subspecies of branch-and-bottleneck, not identical to it. But most uses of branch-and-bottleneck - all the ones I can think of off-hand - end up gravitating towards the delayed-branching model.