Ash'arism vs Muhammadanism

Ash'arism and Muhammadanism both are nouns.

Word	Noun	Adjective	Verb	Adverb
Ash'arism	Yes	No	No	No
Muhammadanism	Yes	No	No	No

As nouns, Muhammadanism is a hypernym of Ash'arism; that is, Muhammadanism is a word with a broader meaning than Ash'arism:

Ash'arism: the classical synthesis of Islamic philosophical theology, formulated by al-Ash'ari.
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

Other hypernyms of Ash'arism include Islam, Islamism, Mohammedanism, Muslimism.

Ash'arism (noun)	Muhammadanism (noun)
the classical synthesis of Islamic philosophical theology, formulated by al-Ash'ari.	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