Copyright of music is complicated because there are two, potentially three copyrights to consider:
For this reason, works that are definitely old enough to be in the public domain (Mozart! Beethovan! Kali Mirza!) are still not able to be used as backgrounds for videos, etc. The reason is vinyl records weren't invented until 1931, and you can only rely on public domain for things published before 1923.
Because of the complexity, most music is published under a "label" which is an organization that owns the copyrights and manages licensing them. There are many commercial services that work with record labels to arrange for permission for large and small licensees.
There are different kinds of licenses:
Only the producer of a film/tv show owns the rights to it. Everyone else involved - actors, animators, designers of props and scenery, people who do CGI and sound effects, even directors (who aren't also the producer) is making a work for hire.
In past that was mostly true in practice, but recent Supreme Court decisions have made it an unambiguous matter of law.
Movies and TV shows are owned by production companies, who manage the licensing for uses like: