Fun fact:

You might know China as 中国

But Chinatown is not China 中国 + Town 城

I never heard of any Chinese diaspora use 中国城

It's always 唐人街 Tang-People Street, Tang referring to China's most powerful dynasty, or 華埠 Hua-City, Hua also refers to Chinese people, it's actually a character in the official name of both PRC 中华人民共和国 (in simplified) and ROC 中華民國 (in traditional)

Overseas Chinese is typically not referred as 中国人 but as 華人 (Hua People)

Chinese Americans are not really referred to as "Americans" but the emphasis is put on the Citizenship, rather than being an "American"

Like in 美籍華人 which Google Translate says is "Chinese American", but really transliterates to "Hua (meaning ethnic Chinese) Person with American Citizenship"

To emphasis on the "American-ness" I'd have to use 華裔美國人 which transliterates to "American of Hua (aka: Chinese) Ethnicity", which I think would sound really weird and I think I'd get weird looks if I use the term 美國人 (American), so I probably would never call myself an "American" in front of Chinese-speaking people, but use 美籍華人 instead.

(Sort of like code-switching. I call myself American in front of other Americans to fit in, but call myself 華人 (ethnic Chinese person) to other ethnic Chinese so I could also fit in.)