IMHO:

- Process: follow it in order when you want result X, all steps need to be completed, each time every time. Routine stuff.

- Runbook: follow it in order when X happens, some steps may not apply depending on the situation or you may need to adapt. Non-routine stuff.

You can have a process without a runbook, but not the reverse. i.e. a process can work, but be undocumented. Whereas having a runbook means you've defined the process (or at least gotten a good start at it..)

Runbooks give more scope to human judgement and experience. But I don't know a formal difference.