falsetto vs head register

falsetto and head register both are nouns.

Word	Noun	Adjective	Verb	Adverb
falsetto	Yes	Yes	No	No
head register	Yes	No	No	No

As nouns, head register is a hypernym of falsetto; that is, head register is a word with a broader meaning than falsetto:

falsetto: a male singing voice with artificially high tones in an upper register
head register: the higher ranges of the voice in speaking or singing; the vibrations of sung notes are felt in the head

Other hypernyms of falsetto include head tone, head voice.

falsetto (noun)	head register (noun)
a male singing voice with artificially high tones in an upper register	the higher ranges of the voice in speaking or singing; the vibrations of sung notes are felt in the head

falsetto (adjective)	head register (adjective)
artificially high; above the normal voice range