No structural difference. The fabric bed of each is identical.
The BB has essentially 3 features. 1 is the net, 2 is the shelf, 3 is the 'footbox'.
The first two of those are self-explanatory, but the third is sometimes misunderstood.
The footbox is a triangular piece of fabric that is sewn to the side of the hammock (on two sides of the triangle). That doesn't affect the lie of the hammock, but it prevents the netting from reducing the room inside the hammock when it is tensioned.
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy