"This disk drive is actually a whole PC" was basically Nintendo's entire Unique Selling Proposition for a long while.

Nintendo made consoles cheaply enough to make a profit, because they weren't designed to be powerful enough for the games that would be released at the end of the console's lifecycle, only the games that would be released near the beginning. But they managed to release games as if the console was more powerful anyway. It was basically because the cartridge was a black box, and could contain anything up-to-and-including its own replacement console. Early-in-lifecycle, game cartridges were just a board with plain ROM chips on it, containing instructions to run on the base hardware; but late-in-lifecycle cartridges included all sorts of other chips. (A game released late in the life of the SNES included a full ARM core, several times more powerful than the SNES's own CPU! Though it only used it to draw a few vector animations in a couple scenes of the game...)

The Famicom Disk System and 64DD were "just" cartridges as well, from their host-console's perspective. And I don't mean that there was a complex dance where the FDS/64DD were running a DOS on the host-console's CPU that sent disk commands back to the drive; that logic was all internal to the drive itself, running on their on-board CPUs. It went even deeper than a memory-mapped IO port or an drive-command wire protocol; the console just didn't direct the drive at all. Rather, the firmware executing on the drive detected when the console would want new data, and DMAed in the required data itself, so that, from the console's perspective, the data was just "there" to see. (A bit like the NES's memory-mapper chips, but for full ROM banks rather than little word-sized windows.)

The closest comparison I can think of to how those devices worked, would be to using one of those aux-to-tape adapters—from the tape reader's perspective, the right data is "just there" when it goes to read it, as if it was a regular tape. In this case, the right data was "just there" in response to bus reads of ROM parts of the memory-space on the cartridge port. These devices were, effectively, the original "flash carts."

This design paradigm has culminated in some pretty ridiculous things embedded into a Nintendo cartridge, actually. There is a Nintendo DS flash cart that embeds a full GBA-compatible CPU core within it. Since it's in the wrong port to deliver GBA games directly to the DS's own GBA-compatible CPU core, it just "brings its own" CPU to emulate them on instead.