Zen Buddhism vs Buddhism

Zen Buddhism and Buddhism both are nouns.

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

As nouns, Buddhism is a hypernym of Zen Buddhism; that is, Buddhism is a word with a broader meaning than Zen Buddhism:

Zen Buddhism: a Buddhist doctrine that enlightenment can be attained through direct intuitive insight
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

As nouns, Buddhism is a hypernym of Zen Buddhism; that is, Buddhism is a word with a broader meaning than Zen Buddhism:

Zen Buddhism: school of Mahayana Buddhism asserting that enlightenment can come through meditation and intuition rather than faith; China and Japan
Buddhism: a religion represented by the many groups (especially in Asia) that profess various forms of the Buddhist doctrine and that venerate Buddha

Zen Buddhism (noun)	Buddhism (noun)
a Buddhist doctrine that enlightenment can be attained through direct intuitive insight	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
school of Mahayana Buddhism asserting that enlightenment can come through meditation and intuition rather than faith; China and Japan	a religion represented by the many groups (especially in Asia) that profess various forms of the Buddhist doctrine and that venerate Buddha