half-mast vs half-staff

half-mast and half-staff both are nouns.

Word	Noun	Adjective	Verb	Adverb
half-mast	Yes	No	No	No
half-staff	Yes	No	No	No

As nouns, half-mast and half-staff are synonyms defined as:

half-mast and half-staff: a position some distance below the top of a mast to which a flag is lowered in mourning or to signal distress

half-mast (noun)	half-staff (noun)
a position some distance below the top of a mast to which a flag is lowered in mourning or to signal distress	a position some distance below the top of a mast to which a flag is lowered in mourning or to signal distress