Muhammadanism vs Shiism

Muhammadanism and Shiism both are nouns.

Word	Noun	Adjective	Verb	Adverb
Muhammadanism	Yes	No	No	No
Shiism	Yes	No	No	No

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

Muhammadanism: 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
Shiism: the branch of Islam that regards Ali as the legitimate successor to Mohammed and rejects the first three caliphs

Other hyponyms of Muhammadanism include Mahdism, Salafi movement, Salafism, Wahabism, Wahhabism, Alawism, Ash'arism.

Muhammadanism (noun)	Shiism (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	the branch of Islam that regards Ali as the legitimate successor to Mohammed and rejects the first three caliphs