Backing up HighSierra & Catalina volumes
 

My MBAir has two volumes on its internal SDD: one with OS High Sierra and the other with OS Catalina.

I want to confirm that the proper way to back up each with SD is to create/run the backup for each OS individually when booted into that OS. I.e., I would not run a backup of Catalina (which appears as its two volumes) when I'm running High Sierra.

And on the external drive (APFS) that is the target, would I have a single Container, with multiple Volumes defined? (Or multiple Containers, each with a Volume for the corresponding source??)

Thank you.

That would, generally, be the right thing to do - with separate volumes, backed up from the real OS.

And should I set up separate APFS Containers -- one Container to hold one Volume -- or have the multiple Volumes in a single Container?

You should use a single container in general.