I think there's a rather liberal definition of "reboot" developing in this thread...
Drastic changes, the presence of inconsistencies, or general reinvigoration do not a reboot make.
For lack of a better source, Wikipedia describes a reboot as "...a discarding of much or even all previous continuity in the series, to start anew." I think that's generally what's understood by the term in this context.
In fandom, perhaps. Among creators, no. As I explained above, the fan perception of "reboot" is based largely on a single example,
Battlestar Galactica. But within the industry, terms such as "reboot" and "reimagining" are used more broadly.
You can't always trust fan interpretations of a term. Look at "remaster." This is a common term that means to go back to the original master copy of a film or recording and make a new print that is as close to the original's quality as possible. But because TOS Remastered included the addition of new visual-effects shots, fandom bizarrely took this familiar decades-old term, completely forgot what it actually means, and began assuming that it meant replacing old footage with new footage -- which is essentially the
exact opposite of what it means. The new FX scenes in TOS-R are the only parts of it that
aren't remastered, because they aren't taken from the original masters. So I'm sorry, but what's "generally understood" often has very little connection to the truth.
It's important to understand that terms like "reboot" and "reimagining" and the like are not technical terminology in the first place. They're idioms and catchphrases. Literally, rebooting is restarting a computer that's been shut down. Applied to a fictional franchise, "reboot" is only a metaphor, a rough analogy, not a formal technical term. So naturally it's going to be used different ways by different people. It's somewhat misguided to insist on a single narrow definition.
And fans obsess more about continuity than industry professionals do. If you're a studio executive or a movie/TV producer, your priority is not going to be the internal continuity and consistency of a fictional universe; your priority is going to be on more practical matters like how successful your property can be, how effective it will be at appealing to an audience and making a profit. So it naturally follows that producers and executives who talk about "rebooting" a franchise are going to be using that in terms of taking something that's not drawing an audience and giving it a fresh start that will draw an audience again. In those terms, it doesn't matter one bit whether it's in the same continuity or a different one. Either approach can be used to make a franchise fresh and successful again. So it's not a question of whether the definition is "liberal," it's a question of whether it makes sense in the terms that the industry professionals using the metaphor would consider important. That's why you can't assume that if a producer or executive uses the term "reboot" or "reimagining" in an interview, it's some kind of code phrase meaning that the old continuity has been tossed out the window. These aren't terms that have formalized, rigid definitions. They're jargon and metaphor.