Well, true, 'PGMusic' produced both programs, but they are two different programs with a long history, written by two different people that got connected later and started merging ideas.
PG (Peter Gannon) I believe is the original author for BiaB, but Jeff Yankauer is for PT (Powertracks) which eventually morphed into RB.

BiaB is and always has been a quick great arrangement/accompaniment tool.
RB used to be a multi-track DAW (PT) but has evolved and now incorporates BiaB features in a more DAW like setting.

In some ways RB is better, one of them being routing options for MIDI and Audio.
Another is RB has more tracks to work with (48 vs 8). And they can be Audio or MIDI, doesn't matter.

I'm probably different than most; I was a long time PT user before RB came out. RB is what made me take the time to see what BiaB could really do; it is faster at some things. I had owned it but not used it much.

TBH, once RB came out, I found it fit my workflow very well and I started looking closer at the BiaB features.
Some people start the other way; they use BiaB most first.
Since I was already a PT user I was drawn to RB a LOT, and BiaB use was pretty sparse, until I caught on to the things it does do better.

I do not work here, but the benefits are still awesome
Make your sound your own!