If you're talking about 4 fonts only that are B-1, B-2, B-3, B-4?

These are Filmotype fonts that were given letters & numbers by VGC when they pirated a substantial number of them. Their original names were attached by someone going through a dictionary and just picking arbitrary words for Filmotype fonts that were initially just letters and numbers also. When and where I haven't the vaguest idea. But for Typositor operators there was always a haphazard list that you had to find out which was which when you bought from VGC.

B-1 = Galaxy
B-2 = Gable
B-3 = Garfield
B-4 = Gamma

There is a complete listing of the VGC letter/numbers = Filmotype names in the Babel Press Type Index which I am still trying to print.
I have found out that (digital) printers want to print so fast that the quality goes down. So far, I have been unable to get this straight.

I just learned about the Bee series at Posterwire, a site dedicated to movie poster design. I'm pretty sure they're different than the series of typefaces mentioned by philippedada. I too would like to know their history, and how close they come to challenging Univers's dominance.

I decided to bump this to see if I get better luck. Yes, Forrest, that is the Bee that we purchased. The version we bought is from URW. They have a pdf of Bee One at:

Bee One from URW

FWIW, the URW Bee fonts do appear to match the ones listed in the Solotype catalog as Galaxy, Gable, Garfield, and Gamma.