A: and B: were not specific to the type of drive. It was common to have two drives before fixed storage became common, often you would have the application disk in one and your data disk in the other though there were other common use patterns for two drives also (with the OS, or at least the core of it, resident in memory you can copy and otherwise manage data over two data disks, and so on).

The first hard-drive in a system was made C: to reserve A: and B: in part because there was software out there that assumed A: and B: were floppy drives and could cause problems if something else was allocated to those signifiers. There are many things that are due to long forgotten compatibility issues like this (try naming file LPT1 under Windows to see another). Another reason is that the BIOS on many PCs was just hard-wired to assume two floppy drives so DOS would see that even if there were no drives really there.

From what I recall from the time I still used MS-DOS, even if you only have one floppy disk drive, it's accessible as both A: and B: and it prompts you to insert the other floppy disk when you change the drive letter. That is, it's "virtualizing" two floppy disk drives using a single physical one. That explains why the first hard disk drive was always C: even when you only had one floppy disk drive (and of course you had at least one floppy disk drive, how could you use a computer without one?)

I thought MS-DOS had special handling for A: and B: since it allowed you to copy from A: to B: even with just one floppy drive.