part-singing vs singing

part-singing and singing both are nouns.

Word	Noun	Adjective	Verb	Adverb
part-singing	Yes	No	No	No
singing	Yes	Yes	No	No

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

Other hypernyms of part-singing include vocalizing.

part-singing (noun)	singing (noun)
singing with three or more voice parts	the act of singing vocal music
	disclosing information or giving evidence about another

part-singing (adjective)	singing (adjective)
	smooth and flowing