Both are display servers which is software that allows programs to write to the screen. X is older and was created back in 1984 at MIT and Wayland is a much newer protocol that is designed to work better on newer (post 90’s) hardware.

The biggest difference is that Wayland basicly allows your desktop direct access to the screen and X has a server that runs and allows your desktop to connect to it. X was originally designed to run remotely as back in the day there was one big commuter that many people connected to.

If this is all very confusing you probably should just stick to your distros defaults. Most of the time you don’t need to care.

For a user: In Wayland programs are supposed to draw their own title bar. Java aplications and old applications must use a backwards compatibility layer that can cause flicker and bad font rendering. The terminology is different (compositor = window manager). Some niche new programs may only run on Wayland. Wayland hasn’t been adopted by BSD (AFAIK).

For a programners: Wayland has more modern, tidy code, but not all toolkits support it natively and few are easy. If you code exclusively for Wayland, a lot of users won’t use your program at the moment.