full moon vs full phase of the moon

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

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

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

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

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

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