Fantastic Beasts and Where to Find Them is an expansion of the Harry Potter world, one that acts as a prequel to the book and film franchise we already know and mostly love, though we should talk about Chamber of Secrets at some point. More pragmatically, it's an opportunity for Warner Bros. to keep selling us movies based on J.K. Rowling's work now that the Potter books that served as the source material are done.
One of the key persistent components of the Fantastic Beasts marketing campaign has been its frequent intonation of this being "From J.K. Rowling's Wizarding World," an attempt to draw the connection between this movie and those that have come before it. Without any characters carrying over from the previous stories, there needed to be some brand continuity, and the "Wizarding World" phrasing not only brings connotations of the earlier movies but also ties in nicely with the Wizarding World of Harry Potter attraction at Universal Studios.
Franchise extensions like these and others are great ways for writers and directors to tell additional stories in universes they've already created. They're also a great way for studios to print some (presumably) easy money, even if the original stars are no longer available or interested in returning.
There are three key ways that modern movie spin-offs have been presented to the audience, with each one tackling the question of brand continuity and audience recognition a bit differently.
1) Create Recognizable Situations
No one really came out of the Jim Carrey vehicle Bruce Almighty crowing about the bit part of Evan Baxter, played by Steve Carell. But that wasn't going to stop Universal from doing what they could to keep the Almighty series going, this time elevating Carell's Baxter to a starring role. While the trailer does actually position this as the "next chapter in the almightiest story of all" and name-drops the first movie (in addition to carrying over Morgan Freeman as God), it doesn't actually draw any connection between the stories of the two movies or position it as the same character being played by Carell.
—The Bourne Legacy
When Matt Damon wasn't excited about returning to the Jason Bourne franchise a few years ago, the studio created a new character played by Jeremy Renner in The Bourne Legacy. The setup in the trailer, though, is very similar, as we see Renner's character recruited for some sort of super-secret government program to turn him into the ultimate weapon, with that plan eventually going sideways on everyone. There are even frequent intonations in the trailers of Bourne and how this is just like the program that made him but better, which is also the pitch the studio is making to the audience.
2) Focus on the Breakout Stars
—Get Him to the Greek
Russell Brand made a huge impression when he played a bit part Forgetting Sarah Marshall, which actually starred Jason Segal and Kristen Bell. His was the performance everyone was talking about, which made it super understandable when he got his own starring vehicle playing the same character, out-of-control rock star Aldous Snow, two years later. Interestingly, the trailer doesn't create any connection between it and the previous movie, instead opting to sell it purely on Brand's performance, along with that of franchise newcomer Jonah Hill.
Similarly, Tommy Lee Jones was the part of 1993's The Fugitive that no one could forget, turning the actor into a headliner overnight. But it would be five years before Chief Deputy Marshal Samuel Gerard got his own story. The connections between this movie and the previous one are much more explicit here, with the trailer starting out with scenes from The Fugitive. That's followed by a new scene that directly echoes the famous "Hard target search of every gas station, residence…" speech Jones gives in the first movie.
3) Actually Sell It as Kind of a Sequel
—This Is 40
While Pete and Debbie (Paul Rudd and Leslie Mann) had only a few minutes of screen time in 2007's Knocked Up, writer/director Judd Apatow obviously felt there was more to their story he wanted to tell. After five years, what were the odds anyone would remember what their characters were called, though? The trailer for This Is 40 refers to it as a "pseudo-sequel" to the Seth Rogen/Katherine Heigl romantic comedy, allowing the audience to draw some form of connection between the two movies without promising it actually continues the primary story from the first one.
While the story connection between this and Finding Nemo isn't stated explicitly in the trailer, it's easy to draw the assumption that this movie picks up mere moments after the events of the first one. If nothing else, the fact that Nemo and his dad are together here should make that clear. So the pitch to the audience is not only that they can return to recognizable and enjoyable characters, but also pick up a story that was dropped over a decade ago and take a familiar trip with them.