Carmelite order vs Order of Our Lady of Mount Carmel

Carmelite order and Order of Our Lady of Mount Carmel both are nouns.

Word	Noun	Adjective	Verb	Adverb
Carmelite order	Yes	No	No	No
Order of Our Lady of Mount Carmel	Yes	No	No	No

As nouns, Carmelite order and Order of Our Lady of Mount Carmel are synonyms defined as:

Carmelite order and Order of Our Lady of Mount Carmel: a Roman Catholic mendicant order founded in the 12th century

Carmelite order (noun)	Order of Our Lady of Mount Carmel (noun)
a Roman Catholic mendicant order founded in the 12th century	a Roman Catholic mendicant order founded in the 12th century