The other night, I got into a discussion with a friend regarding movies-- specifically sequels and reboots. When I told her they were in the process of getting another Spider-Man film going, her response was: "Oh hell! Not another sequel! Don't we have enough of those?" This got me thinking. What, if any, is the difference between a sequel, continuation, and a reboot? I may be stating the obvious here, but I actually learned something.
By definition, a continuation is "something that continues some preceding thing by being of the same kind or having a similar content." Along the same line, a sequel is "a literary work, movie, etc., that is complete in itself but continues the narrative of a preceding work." A reboot, depending on who you are, is either a waste of time or a necessity. I guess that depends on the franchise?
Anyway...It seems that most people interchange the two terms (sequel and continuation) thinking they mean the same thing, but obviously not. I want to give some examples of movie series for each of these types to help clarify the difference.

First off, if you look at the "Lord of the Rings" series, a lot of people consider the second and third films to be sequels, but by definition, I would label them as continuations. The three films are essentially one really long film which is then separated into three shorter films. If you were to watch "Return of the King" as a stand-alone film, and having no knowledge of the series, you would more than likely be confused as to who the characters were and where the storyline has been and will be going; nothing would make sense. A continuation requires that the previous films would, for the most part, have to be viewed to understand characters, plots, etc. Another example of this film type would be the Harry Potter films. In order to understand why this kid with a lightening bolt on his forehead is so angry with a lizard looking dude, one would have to view the previous films to really understand the idea and the characters of the the series.

Now, as far as sequels go, let's look at a series like "Spider-Man." In reference to the definition above, each of the films is complete, meaning it has a beginning, middle, and an end. Yet the two later films feed off the first, using the same characters and its events. A majority of film series falls into this category, especially comic book films.
You could also argue that sequels could be a sub-category of continuations in that the stories from the first film will at times spill over into the subsequent films, such as the "love story" between Peter Parker and Mary Jane. But ultimately, it is still a sequel.
As for reboots, check out my article titled "Reboot? Remake? Reinvent? Leave it alone?" for my take on that one.
There you have it. Like I said, I may be stating the obvious, but there is your useless information for the day.
Thank you to dictionary.com for the use of their "definitions."