And while we're on the subject...
Say, Darling! is often described as a musical, thanks to an original cast recording with a full orchestration by Sid Ramin. But it was not heard that way in the theatre (I believe it was performed onstage with one or two pianos), and those songs are songs within the fictional musical being produced within Say, Darling! The show is probably a better candidate for that hybrid category: play with songs.
"Gif me the cobra jool!"