Muslimism vs Mahdism

Muslimism and Mahdism both are nouns.

Word	Noun	Adjective	Verb	Adverb
Muslimism	Yes	No	No	No
Mahdism	Yes	No	No	No

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

Muslimism: the monotheistic religious system of Muslims founded in Arabia in the 7th century and based on the teachings of Muhammad as laid down in the Koran
Mahdism: belief in the appearance of the Mahdi; devotion to a Mahdi

Other hyponyms of Muslimism include Salafi movement, Salafism, Shiism, Wahabism, Wahhabism, Alawism, Ash'arism.

Muslimism (noun)	Mahdism (noun)
the monotheistic religious system of Muslims founded in Arabia in the 7th century and based on the teachings of Muhammad as laid down in the Koran	belief in the appearance of the Mahdi; devotion to a Mahdi
the civilization of Muslims collectively which is governed by the Muslim religion