I may be able to help out here a bit, I've done a lot of testing and production backups to B2.
Naming wise, Olivier is right, B2 is "S3 Compatible" which is why it works but it's not "officially" supported in that way. However since the S3 compatibility "layer" in B2 has been super solid, backing up to it using S3 protocol should be fine.
As for your question about differentials, whatever backup jobs you setup are what will be put in B2. So if you setup full backups and select B2 as the remote for it, then it's full backups, etc....
I would recommend having your B2 backups be a different job than any local backups though (if you're doing local for faster restore), it's nice having control separately.