^ I'm not at all sure that fans are the only ones who think about these things. Fans aren't the ones, for example, that popularized the "reboot." Creators did, or at least studios and producers.
True, but they don't define the term the same way. Fans have gotten this notion into their heads that "reboot" means a complete restart of the continuity, because that's the way Battlestar Galactica did it. Just because one prominent reboot did that, they assume that defines the whole term, which doesn't make any logical sense. But in the industry, whether two works are in the same continuity doesn't matter as much as whether a franchise is commercially successful. A reboot, in industry terms, is any reinvention or revitalization of a dormant franchise in order to make it commercially viable again. This can be a reinvention in the sense of starting completely over like BSG or the Bionic Woman remake, or it can be a reinvention in the sense of continuing the original continuity with a fresh style and attitude like Doctor Who, or it can be something in between like Star Trek, an alternate timeline spun off from the original, at once an outgrowth of the old continuity and a fresh start. As I said, continuity is just a tool in the box. Fans focus much more on drawing these arbitrary distinctions and labels, because as outside observers, they have the luxury of dwelling on such matters. The people actually making the works and hoping to profit from them have many more pressing concerns to occupy them than whether story X is exactly consistent with story Q. They will use continuity to the extent that it serves their more urgent priorities, like telling a good story and making the property financially successful. Continuity is a tool, not a straitjacket.