fairy circle vs fairy ring

fairy circle and fairy ring both are nouns.

Word	Noun	Adjective	Verb	Adverb
fairy circle	Yes	No	No	No
fairy ring	Yes	No	No	No

As nouns, fairy circle and fairy ring are synonyms defined as:

fairy circle and fairy ring: a ring of fungi marking the periphery of the perennial underground growth of the mycelium

fairy circle (noun)	fairy ring (noun)
a ring of fungi marking the periphery of the perennial underground growth of the mycelium	a ring of fungi marking the periphery of the perennial underground growth of the mycelium