full phase of the moon vs full-of-the-moon

full phase of the moon and full-of-the-moon both are nouns.

Word	Noun	Adjective	Verb	Adverb
full phase of the moon	Yes	No	No	No
full-of-the-moon	Yes	No	No	No

As nouns, full phase of the moon and full-of-the-moon are synonyms defined as:

full phase of the moon and full-of-the-moon: the time when the Moon is fully illuminated

Other synonyms of full phase of the moon include full, full moon.

full phase of the moon (noun)	full-of-the-moon (noun)
the time when the Moon is fully illuminated	the time when the Moon is fully illuminated