firmament vs vault of heaven

firmament and vault of heaven both are nouns.

Word	Noun	Adjective	Verb	Adverb
firmament	Yes	No	No	No
vault of heaven	Yes	No	No	No

As nouns, firmament and vault of heaven are synonyms defined as:

firmament and vault of heaven: the apparent surface of the imaginary sphere on which celestial bodies appear to be projected

Other synonyms of firmament include celestial sphere, empyrean, heavens, sphere, welkin.

firmament (noun)	vault of heaven (noun)
the apparent surface of the imaginary sphere on which celestial bodies appear to be projected	the apparent surface of the imaginary sphere on which celestial bodies appear to be projected