Is testing based on API a black-box test or a grey-box test?

Is testing based on an API (like a Javadoc) a black box or grey box test?

What I think

I think it is grey box, testing.

Why

1. Black box test is when we DONT have knowledge of the system and its inner workings. However since we are given the API, we know the return types, the parameters passed, etc we have general albeit basic understanding of what each method should do and the inner workings of the system.

Also if you recall the meaning of grey box testing : A test is designed based on the knowledge of algorithm, architectures, internal states, or other high -level descriptions of the program behavior.

Since we have the API, we can design some test cases, which will be of relatively high/medium coverage.