Chinese vs Taiwanese

Chinese and Taiwanese both are nouns.

Word	Noun	Adjective	Verb	Adverb
Chinese	Yes	Yes	No	No
Taiwanese	Yes	Yes	No	No

As adjectives, Chinese and Taiwanese are synonyms defined as:

Chinese and Taiwanese: of or relating to or characteristic of the island republic on Taiwan or its residents or their language

Other synonyms of Chinese include Formosan.

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

Chinese: any of the Sino-Tibetan languages spoken in China; regarded as dialects of a single language (even though they are mutually unintelligible) because they share an ideographic writing system
Taiwanese: any of the forms of Chinese spoken in Fukien province

Chinese (noun)	Taiwanese (noun)
any of the Sino-Tibetan languages spoken in China; regarded as dialects of a single language (even though they are mutually unintelligible) because they share an ideographic writing system	any of the forms of Chinese spoken in Fukien province
a native or inhabitant of Communist China or of Nationalist China	a native or inhabitant of Taiwan

Chinese (adjective)	Taiwanese (adjective)
of or pertaining to China or its peoples or cultures	of or relating to or characteristic of the island republic on Taiwan or its residents or their language
of or relating to or characteristic of the island republic on Taiwan or its residents or their language