tai chi chuan vs martial art

tai chi chuan and martial art both are nouns.

Word	Noun	Adjective	Verb	Adverb
tai chi chuan	Yes	No	No	No
martial art	Yes	No	No	No

As nouns, martial art is a hypernym of tai chi chuan; that is, martial art is a word with a broader meaning than tai chi chuan:

tai chi chuan: 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

tai chi chuan (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