Order of Our Lady of Mount Carmel vs Carmelite order

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

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

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

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

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