Buddhism vs Zen

Buddhism and Zen both are nouns.

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

As nouns, Zen is a hyponym of Buddhism; that is, Zen 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
Zen: a Buddhist doctrine that enlightenment can be attained through direct intuitive insight

As nouns, Zen is a hyponym of Buddhism; that is, Zen 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
Zen: school of Mahayana Buddhism asserting that enlightenment can come through meditation and intuition rather than faith; China and Japan

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

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