It apparently stands for Big British. It's somewhat of a blend between a TS and a Marshall Amp In A Box (note - even though the Bluesbreaker was initially a Marshall pedal and named after a Marshall amp, it's not a Marshall Amp in a box pedal; it's its own animal). The BB is probably a little closer to an OCD with a bit more mids. I personally love Bluesbreaker-style pedals, but different strokes for different folks! I personally don't really like Tubescreamers (shock, horror).