Other than the older MUDs where usually text based rather than having real-time graphics?
It really is just a matter of degree. Both tend to follow the same sorts of gameplay (turn-based or tick-based combat, experience, leveling up, equipment, skills), with some variations of course.
However, MUDs are text-based, built by volunteers (I’ve never heard of a commercial MUD; closest I’ve seen is one that runs on donations), and usually has few players (it was and is rare to have more than 100, even before MMOs hit the spotlight). They’re usually free to play.
MMORPGs are graphical, usually built by companies although there are quite a few volunteer efforts out there these days, and usually have a lot of players, generally in the thousands and going up. They’re usually subscription-based.
Looking at it cynically, MUDs are created as a hobby and MMORPGs are created for profit (with exceptions, as always). But gameplay wise? There’s really not that much difference.