About the naming, yes, what you describe is exactly called first and second endings. In notation, the first ending has a repeat sign at the end. You jump back to the first repeat sign that BIAB calls Bar at Beginning of Chorus or something like that - the first number AudioTrack flagged. The second ending has a double bar line at the end but no repeat sign, so you keep playing into the next part of the song.

In BIAB I normally do not try to do this song structure; I duplicate the measures and play one longer song form.

You might also be thinking of a Coda, as in, during the last time through the song, jump to the Coda to play an ending section. I use the Tag function in BIAB for those.

BIAB 2025 Win Audiophile. Software: Studio One 7 Pro, Swam horns, Acoustica-7, Notion 6, Song Master Pro, Win 11 Home. Hardware: Intel i9, 32 Gb; Roland Integra-7, Presonus 192 & Faderport 8, Royer 121, Adam Sub8 & Neumann 120 monitors.