Wesleyan vs Methodist

Wesleyan and Methodist both are nouns.

Word	Noun	Adjective	Verb	Adverb
Wesleyan	Yes	Yes	No	No
Methodist	Yes	Yes	No	No

As adjectives, Wesleyan and Methodist are synonyms defined as:

Wesleyan and Methodist: of or pertaining to or characteristic of the branch of Protestantism adhering to the views of Wesley

As nouns, Methodist is a hypernym of Wesleyan; that is, Methodist is a word with a broader meaning than Wesleyan:

Wesleyan (noun)	Methodist (noun)
a follower of Wesleyanism	a follower of Wesleyanism as practiced by the Methodist Church

Wesleyan (adjective)	Methodist (adjective)
of or pertaining to or characteristic of the branch of Protestantism adhering to the views of Wesley	of or pertaining to or characteristic of the branch of Protestantism adhering to the views of Wesley