singing vs vocal music

singing and vocal music both are nouns.

Word	Noun	Adjective	Verb	Adverb
singing	Yes	Yes	No	No
vocal music	Yes	No	No	No

As nouns, vocal music is a hypernym of singing; that is, vocal music is a word with a broader meaning than singing:

singing: the act of singing vocal music
vocal music: music that is vocalized (as contrasted with instrumental music)

Other hypernyms of singing include musical performance.

singing (noun)	vocal music (noun)
the act of singing vocal music	music that is vocalized (as contrasted with instrumental music)
disclosing information or giving evidence about another	music intended to be performed by one or more singers, usually with instrumental accompaniment

singing (adjective)	vocal music (adjective)
smooth and flowing