Islamism vs Mahdism

Islamism and Mahdism both are nouns.

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

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

Islamism: 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 Islamism include Salafi movement, Salafism, Shiism, Wahabism, Wahhabism, Alawism, Ash'arism.

Islamism (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
a fundamentalist Islamic revivalist movement generally characterized by moral conservatism and the literal interpretation of the Koran and the attempt to implement Islamic values in all aspects of life