[voiceofunreason]

That's not quite right, historically.

Behavior Driven Development began as a re-languaging of TDD: "The developers were much more receptive to TDD when I stopped talking about testing." -- Dan North.

BDD diverged from TDD fairly early, after some insights by Chris Matts.

As for TDD advocating tests of the public interface... that seems to me to have been more aspirational than factual. The tests in TDD are written by developers for developers, and as such tend to be a bit more white/clear box than pure interface testing would suggest.

In the edge cases where everything you need for testing is exposed via the "public" interface, these are equivalent, of course, but there are tradeoffs to be considered when the information you want when running isolated experiments on an implementation isn't part of the contract that you want to be supporting indefinitely.