monarchist vs Orleanist

monarchist and Orleanist both are nouns.

Word	Noun	Adjective	Verb	Adverb
monarchist	Yes	No	No	No
Orleanist	Yes	No	No	No

As nouns, Orleanist is a hyponym of monarchist; that is, Orleanist is a word with a more specific, narrower meaning than monarchist:

monarchist: an advocate of the principles of monarchy
Orleanist: a supporter of the Orleans branch of the Bourbons that was descended from a younger brother of Louis XIV

Other hyponyms of monarchist include Cavalier, Royalist.

monarchist (noun)	Orleanist (noun)
an advocate of the principles of monarchy	a supporter of the Orleans branch of the Bourbons that was descended from a younger brother of Louis XIV