t'ai chi vs martial art

t'ai chi and martial art both are nouns.

Word	Noun	Adjective	Verb	Adverb
t'ai chi	Yes	No	No	No
martial art	Yes	No	No	No

As nouns, martial art is a hypernym of t'ai chi; that is, martial art is a word with a broader meaning than t'ai chi:

t'ai chi: a Chinese system of slow meditative physical exercise designed for relaxation and balance and health
martial art: any of several Oriental arts of weaponless self-defense; usually practiced as a sport

t'ai chi (noun)	martial art (noun)
a Chinese system of slow meditative physical exercise designed for relaxation and balance and health	any of several Oriental arts of weaponless self-defense; usually practiced as a sport