BSB certainly is a curiosity – according to Wikipedia, there is no British Standard for it! It's a misnomer.
My 1949 Newnes Engineers Reference calls it 'Standard Brass Thread 55° Whitworth', and – unlike all the other threads listed – doesn't say who set the standard. Looks like an industry convention; "let all threads in brass tube be cut 26tpi in Whitworth Form".
Who knows why Martin's tap and die are labelled BSF? Possibly its because BSB shares many of the same Imperial diameters as BSF. To make a BSB tap, just take ordinary BSF stock and thread it at 26 tpi, job done. Pretty confusing though, sooner or later someone will be baffled by an allegedly BSF tap that wrongly cuts 26tpi!
BSB and BSF are 55° threads, BSC is 60°. For those working on bikes, 5/16" 26tpi BSC is close enough to M8x1.0 to cause accidental interchange problems.
Dave