Never used the Atari's, but for C64, the 1541 floppy contained a full computer not that much less powerful than the C64 itself (less RAM, obviously no sound or graphics; but you could load code onto the 1541 over the serial port and use it as a co-processor...) in addition to the drive mechanics, and that was pretty normal for computers at the time, which explains why floppy drives were so expensive... Looking up the 810, it seems to be a similar-ish full computer.

(I freaked my parents out with experiments like pulling the CPU and IO chips out of their sockets and swapping them to see what would happen; the 1541 has a 6502 CPU instead of the 6510 in the C64, and 6522 IO chips instead of 6526 - the CPU difference is lack of GPIO on the 6502; the 6522 lacks a real-time clock, which next to no software on the C64 uses)