"She speaks Vietnamese because she is Vietnamese."
Translation:Cô ấy nói tiếng Việt tại vì cô ấy là người Việt Nam.
I suppose the difference between "tieng Viet" and "nguoi Viet" is the difference between the Vietnamese language and the Vietnamese ethnicity?
Yes, you are correct.
Tiếng = voice, sound, language.
Người = people, human, person.
I've heard that "người Việt" refers to "Kinh people". They account for 86% of the Vietnamese population, so the expression "người Việt" might exclude the other 14%. It's only my opinion though...
You can say both/use both interchangeably. First one is "a person OF Vietnam" vs. "a Vietnamese person"