Even machine which only have a single floppy drive have both A and B drives. The B drive is a virtual floppy drive which allowed you to make a copy fo a disk, so you could type Copy A:*.* B: and the machine would read the contents of the floppy disk to be copied, then say "Put the destination disk in Drive B:" which was in actual fact the same drive. After inserting a disk the machine would then write out the contents just as if it was writing to a different drive.
I'm not sure what you mean by "why did the 'B' drive come before the 'A' drive?" - it didn't.
Incidentally it wasn't only home machines that didn't have hard drives - business machines often had only one or two floppy drives as well. The first hard drive I ever installed was 5 Megabytes (!) and cost just under �3,000.