Although your question was not not limtited to or only specificed to The X-Men Franchise, I thought I would add some clarity to the X-Men portian.
The main franchise which consists of two (possibly 3 timelines, depending on what is exactly true about Logan's placement) are directly connected to themselves.
Main Films: X-Men, X2, X-Men: The Last Stand, X-Men Origins: Wolverine, X-Men: First Class, The Wolverin, X-Men:Days of Future Past, X-Men: Apocalypse, Logan, X-Men: Dark Pheonix (upcoming)
However, the X-Men spin offs: Deadpool, Legion, and The Gifted are often characterized being in their own separate universes from each other and the main X-Men films -- and DO NOT DIRECTLY Connect.
Landgraf stated, in January 2016, that the series would be set in a
universe parallel to the X-Men films where "the US government is in
the early days of being aware that something called mutants exist but
the public is not".
The producers hoped that audiences would watch the show because of its
character-focus and the talents of Hawley and the cast, rather than to
"see a Marvel franchise show."Donner also noted that having Hawley
focus on Haller's perspective of reality rather than connections to
the X-Men films allowed the series to avoid the convoluted continuity
of the films, "because we play with so many different timelines, and
we rebooted and not really rebooted and all that" throughout the
films. Therefore, "the cinematic universe will not worry about Legion.
They will not worry about these TV worlds at all.
“It’s not in the continuity of those films in the sense that the
current X-Men films take place in a universe where everybody on
planet earth is aware of the existence of mutants. Legion takes place
in a parallel universe if you will where the government is aware
mutants exist but the public is not. I wouldn’t see characters moving
back and forth because they really are parallel universes**.”
The Gifted is an American television series created for Fox by Matt
Nix, based on Marvel Comics' X-Men properties. It is connected to the
X-Men film series, set in an alternate timelinewhere the X-Men have
disappeared. The show is produced by 20th Century Fox Television in
association with Marvel Television, with Nix serving as showrunner.
"What's nice is Deadpool exists in his own universe. He's part of the
larger X-Men universe, but in a way he isn't. He interacts with that
world but he is in the present. We don't deal with the '60s or the
'70s or the future. It's here and now. More than anything, I think
he's going to have his fun with what they do in the other franchise.
But fortunately, we don't have to play by those same rules. Deadpool
is a movie that did break all the rules.
Although there has yet to be any public statement about if New Mutants will also follow suit and be in it's own universe, it seems likely given how they have treated other spin-offs and knowing that, at least before Dinsey's possible merger (it is not yet finalized), it was said to be a "trilogy"
...in May 2015, Fox finalized a deal to have Boone direct The New
Mutants, from a script by himself and Lee, with Kinberg and Lauren
Shuler Donner producing. The film would be a standalone spinoff film,
expanding the universe of the X-Men films. While working on the
first draft of the script, Boone sent it and his ideas for the film to
Sienkiewicz, who thought Boone "had it figured out" but was also not
just copying the comics.
However, there is potential in some of these cases to see "alternate" versions of main X-Men film characters. In earlier development, Professor X was said to be in New Mutants, but James McAvoy has officially shot down rumors of appearing in the film. Noah Hawley, however has stated that he would like get Professor X for Legion, since it is important part of the main character's story in the comics. Season one also heavily referenced Xavier. Hawley says he thinks it's a matter of time, but this was also before the beginnings of Disney's merger...