anthology, omnibus, portmanteau
Anthologies, omnibuses and portmanteaus are very similar to the point where any differences are so subtle as to be interchangeable. Nowadays, in most cases, they are used to mean the same thing and are all part of the same subgenre. It is also possible for a movie to be considered more than one type of anthology style film.
An anthology film is a subgenre of films consisting of several different short films, often tied together by only a single theme, premise, or brief interlocking event such as a narrator. Quite often each story is directed by a different director. (Creepshow 1982, Black Sabbath 1963)
An omnibus is a kind of anthology that often showcases specific directors whose stories are usually connected by a specific theme, premise, event or people. (Dead of Night 1945, Body Bags 1993)
Portmanteau films are anthologies wrapped in a connecting story. (Tales from the Hood 1995, Tales from the Dark Side 1990)
Hyperlink cinema, Compilation film, Composite film, Package film, Revue film
There are other films that can be similar to anthologies but have some distinct differences.
Hyperlink cinema has multiple interwoven story lines, usually with the same characters. It can have plot twists and jumps from one plot to another sometimes with flashbacks or flashforwards. The stories are somewhat separate but influence each other. Sometimes the association isn’t revealed until the end. (Pulp Fiction 1994, Contagion 2011)
A compilation film is a film edited from previously released or archive footage that is compiled in a different way or a new order of appearance. Sometimes it is combined with new footage or commentary but most of the movie is either existing or stock footage. This was done with a lot of the serials. Many were reedited into feature films. Also some television episodes were compiled together to make a feature film. (The Phantom Creeps 1939, any of the Rocky Jones Space Ranger movies)
A composite film is a feature film where two or more separate stories are structured so that they form a continuity that links from one story to the next. The stories are individual yet when connected are part of a greater story. (Sin City 2005, The Canterbury Tales 1972)
Package film is a film consisting of several short films, often a feature length compilation of short subjects in animation. (Fantasia 1940, The Three Caballeros 1944).
A revue is a type of multi-act popular theatrical entertainment that combines music, dance, and sketches. Many musicals came from this type of film. (The Show of Shows 1929, Paramount on Parade 1930).