full-of-the-moon vs full moon

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

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

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

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

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

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