In English, many things fall under the term Chinese, but this is not so in Chinese. I'm just writing what I suggest to use instead of making everything 中國 or 中文, because it's more complicated than that. Obviously I cannot speak for everyone, and others may have other terms they prefer.
華人 is probably the most generic term that can be used to describe a Chinese person, regardless of nationality and immigrant generation status. 華僑 typically means an overseas immigrant who still has their original nationality. 華裔 means a Chinese ethnic background, for example, 華裔美國人 is one way of saying Chinese American.
中文 means Chinese characters specifically, as in the characters and words used to denote what we speak. 文 does mean writing, after all. Spoken Chinese can be 華語 or 漢語, which basically covers all the different dialects or local variants of the spoken language.
國語 is a government connotation. When Taiwan was under Japanese rule, 國語 was Japanese; now under Republic of China rule, 國語 is Mandarin. But the people of Taiwan communicate in so many more dialects and languages.
中文 is the official language in many places: 中國, 香港, 澳門, 臺灣, 新加坡. It is also used by 華人 all over the world. Now what each person identifies as is a matter of their own identity. But don't reduce their identity down to a nationality or broad ethnic group. And furthermore, please don't tell people what they should identify as.
The term Chinese in English often refers to Han culture or language. But in reality, there are different ethnic groups and languages within each place where 中文 is the official language, so that may also play a role in each person's identity.





