Question: what is the difference between bb and bbb?
Answer: You're more or less right, but a BBb tuba is the same thing as a Bb tuba. As in, they are literally the same thing. a Bb tuba is not a baritone horn unless you're still strictly referring to horns by the Helmholtz system. Calling a tuba a Bb tuba is just short hand for calling it a BBb tuba.