FBA is BFT + decentralization. The F stands for "Federated" in contrast to "just" distributed system which are only physically decentral, federated system also decentralize the control.
The key difference is that it does not need a puzzle (and therefore no resource wasting to solve it) to determine who will write the next block but rather BFT is used to agree on the next block. Its quite elegant compared to the puzzle and obviously way more efficient.
