Michaelmas Day vs Michaelmas

Michaelmas Day and Michaelmas both are nouns.

Word	Noun	Adjective	Verb	Adverb
Michaelmas Day	Yes	No	No	No
Michaelmas	Yes	No	No	No

As nouns, Michaelmas Day and Michaelmas are synonyms defined as:

Michaelmas Day and Michaelmas: honoring the archangel Michael; a quarter day in England, Wales, and Ireland

Other synonyms of Michaelmas Day include September 29.

Michaelmas Day (noun)	Michaelmas (noun)
honoring the archangel Michael; a quarter day in England, Wales, and Ireland	honoring the archangel Michael; a quarter day in England, Wales, and Ireland