In a nutshell BiaB is for writing songs
Realband is for recording.

Realband started out as Powertracks. It is a 48 track recording software at its core.
If you had a 6 piece band, say a couple guitars, bass, drums, keyboards and vocalist, and wanted to record them.
I suppose you could try to use a mixer and get the tracks mixed to one stereo input and record them in BiaB.
But if you wanted to record each of those players to their own track Realband is the better choice.

You could even record the each of the acoustic drums to their own track. Then go back and let one of the guitar players record a solo, and then let the vocalist record some harmonies.. etc.

They recently added the BiaB features to Powertracks and called it Realband.
So if the band showed up and the drummer couldn't make it; no problem.
You can generate a Realdrum track for them to play along with. Then go back later (when that lazy drummer shows up) and have him record his drum part.
If you think of it in terms of audio, Realband, with its mixer and multiple audio tracks is much different than BiaB.

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