theme song vs signature tune

theme song and signature tune both are nouns.

Word	Noun	Adjective	Verb	Adverb
theme song	Yes	No	No	No
signature tune	Yes	No	No	No

As nouns, theme song and signature tune are synonyms defined as:

theme song and signature tune: a melody used to identify a performer or a dance band or radio/tv program

Other synonyms of theme song include signature.

theme song (noun)	signature tune (noun)
a melody that recurs and comes to represent a musical play or movie	a melody used to identify a performer or a dance band or radio/tv program
a melody used to identify a performer or a dance band or radio/tv program