Right. The vast majority of movies have background music, but we don't call them "musicals".
I guess there are a few different kind of movie musicals, I'm just wondering if there are terms for each of them: we've got typical "musicals" (ala Elvis movies), then we've got "operas" (where virtually the entire story is told through song, ala The Umbrellas of Chambord), then we've got movies about music (this is where I'm wondering if there's a term for them) that feature music, but don't present it in the way typical musicals do.
I'd like to say that That Thing You Do is a musical bio-pic (which is a substantial category itself), but since it's fiction, I don't know if the term "bio-pic" would apply. (???)
Then I wonder how Fantasia (1940) would be classified? It's all music (no spoken words), but not exactly an opera. (I believe it's entirely instrumental as well.) "Animated Musical Anthology?"
I don't know the exact terms for each type of musical, but I found this article that explains some of the different types of musicals. (I think it's mainly about Broadway musicals, but it gives you an idea of the different types of musicals.)
https://www.superprof.co.uk/blog/types-of-musicals/
Book Musicals - Musicals with a strong narrative structure, where songs and dances are fully integrated into a story. ("Les Misérables", "The Phantom of the Opera", "West Side Story")
Revue Musicals - A collection of songs, dances, and sketches, often without a unifying plot, focusing on a theme or composer. ("Ain't Misbehavin'", "Fosse", "Smokey Joe's Cafe")
Jukebox Musicals - Musicals that use previously released popular songs from a particular artist or genre, woven into a narrative. ("Mamma Mia!", "Jersey Boys", "We Will Rock You")
Film Musicals - Musicals originally created for film, often adapted into stage productions later, or vice versa. ("The Lion King", "Hairspray", "The Producers")
Concept Musicals - Musicals where the show's message or theme is more important than the narrative, often experimental in nature. ("Cats", "A Chorus Line", "Company")
Pop/Rock Musicals - Musicals that feature contemporary pop or rock music, often appealing to a broader, younger audience. ("Rent", "American Idiot", "Hamilton")
They are all explained in much more detail in the article.