head voice vs head register

head voice and head register both are nouns.

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

As nouns, head voice and head register are synonyms defined as:

head voice and head register: the higher ranges of the voice in speaking or singing; the vibrations of sung notes are felt in the head

Other synonyms of head voice include head tone.

head voice (noun)	head register (noun)
the higher ranges of the voice in speaking or singing; the vibrations of sung notes are felt in the head	the higher ranges of the voice in speaking or singing; the vibrations of sung notes are felt in the head