Chinese vs Hakka

Chinese and Hakka both are nouns.

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

As nouns, Hakka is a hyponym of Chinese; that is, Hakka 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
Hakka: a dialect of Chinese spoken in southeastern China by the Hakka

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

Chinese: a native or inhabitant of Communist China or of Nationalist China
Hakka: a member of a people of southeastern China (especially Hong Kong, Canton, and Taiwan) who migrated from the north in the 12th century

Other hyponyms of Chinese include Chinaman, chink, Boxer, mandarin.

Chinese (noun)	Hakka (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	a dialect of Chinese spoken in southeastern China by the Hakka
a native or inhabitant of Communist China or of Nationalist China	a member of a people of southeastern China (especially Hong Kong, Canton, and Taiwan) who migrated from the north in the 12th century

Chinese (adjective)	Hakka (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