They don't necessarily mean what you'd like them to, though, nor are they unambiguous.
"Reboot" in the literal sense doesn't have a thing to do with entertainment.
I think though that there is a consensus on what it means and the origins of the term. It's pretty basic in that reboot is equated with starting over. Your computer is the same, the hardware is the same, the software is the same, but the memory has been wiped. In that analogy, memory is continuity or "canon," and that's how it has often been applied. Of course, this usage does become ambiguous like you say, but only because people misuse it or draw the analogy to something other than continuity. Or they don't quite understand the computer terminology, which is understandable.
There are plenty of things which often accompany a continuity reboot that don't necessarily make it one in itself, like making changes to designs to be contemporary. There aren't very many continuity reboots that don't do this, but there are plenty of continuations that do. If we were to go back to the analogy of computers, that would probably be like updating an operating system or even just changing the computer's appearance theme. A reboot in itself would not do these things.
From a computing standpoint, there really isn't such a thing as a partial reboot or "reboot to an extent." The term used in these situations is typically just retroactive or selective continuity, trying to maintain the illusion of one coherent continuity. That's what all of the Trek spin-offs used. It's probably what a new show would do too if it doesn't indeed reboot.