"We are American."
Translation:Chúng tôi là người Mỹ.
Mỹ is the shorthand version of Mỹ Lợi Gia, a Chinese loanword 美利加 (Mei Li Jia) that in turn derived from 'America'. In both languages, it's shortened to just the first syllable (Nước Mỹ and Meiguo), which just happened to be the second syllable in America, 'Mer'.
Generally, from experience, it means the United States.
There is a difference or nuance between the two. "Chúng tôi" refers to ourselves when speaking to a second party (i.e., to someone else) whereas "chúng ta" refers to ourselves when speaking among ourselves.
In other words, we are "chúng ta" to ourselves and "chúng tôi" to other people.
There are other variations as well but that would be another post.