I'm confused about these phrases.
- Does "Indian-born Chinese" mean that you live in India, and were born in China?
- Does "Chinese-born Indian" mean that you live in China, and were born in India?
The "meaning changes a lot" because in English, word order is critically important to grammar. In some languages, you can change the order of words in nearly limitless ways without changing the meaning. But English doesn't have (many) inflections, so word order does the work.
In English, adjectives usually precede the noun they modify. So:
indicating a Chinese person who was born in India. Putting the same words in a different order give:
or an Indian person who was born in China. The hyphen also gives a clue in this case; hyphens are often used within multi-word adjectives.
An "Indian-born Chinese" person is a person who is Chinese, and was born Indian.
The hyphen binds the term "born" to "Indian". Without the hyphen, it's a bit ambiguous, but I think most people would interpret it the same way. Note that a comma would have the opposite effect: "He is Indian, born Chinese".
So then, what does it mean to "be" Chinese and "be born" Indian? That's a little trickier.
"Chinese" could mean
or maybe even
"Indian-born" could mean
It probably would not mean born ethnically Indian, because one's ethnicity doesn't change so there is no need to qualify it with "born".