It's an interesting level of abstraction question. On a fine-grained level, yes, BTC works algorithmically as you have pointed out, and FFT is not the exact same thing as BTC. The question the is whether either of these things work socially / for society.

Whether it's accurate or not, I imagine non-experts would regard the difference between BTC and FFT as pretty negligible, perhaps akin to the difference between "social media" and IG vs. Reddit.