Buddhism vs Mahayana

Buddhism and Mahayana both are nouns.

Word	Noun	Adjective	Verb	Adverb
Buddhism	Yes	No	No	No
Mahayana	Yes	No	No	No

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

Buddhism: the teaching of Buddha that life is permeated with suffering caused by desire, that suffering ceases when desire ceases, and that enlightenment obtained through right conduct and wisdom and meditation releases one from desire and suffering and rebirth
Mahayana: one of two great schools of Buddhist doctrine emphasizing a common search for universal salvation especially through faith alone; the dominant religion of China and Tibet and Japan

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

Buddhism: a religion represented by the many groups (especially in Asia) that profess various forms of the Buddhist doctrine and that venerate Buddha
Mahayana: a major school of Buddhism teaching social concern and universal salvation; practised in China, Japan, Tibet, Nepal, Korea, Mongolia

Other hyponyms of Buddhism include Zen, Zen Buddhism, Hinayana, Tantrism.

Buddhism (noun)	Mahayana (noun)
the teaching of Buddha that life is permeated with suffering caused by desire, that suffering ceases when desire ceases, and that enlightenment obtained through right conduct and wisdom and meditation releases one from desire and suffering and rebirth	one of two great schools of Buddhist doctrine emphasizing a common search for universal salvation especially through faith alone; the dominant religion of China and Tibet and Japan
a religion represented by the many groups (especially in Asia) that profess various forms of the Buddhist doctrine and that venerate Buddha	a major school of Buddhism teaching social concern and universal salvation; practised in China, Japan, Tibet, Nepal, Korea, Mongolia