Is C++ STL a C++ API?

We have an assignment wherein we have been forbidden to use any C++ API. So, this brings me to the following questions:

1. What exactly is the difference between a library and an API?
2. Is the C++ STL (http://ift.tt/1D0nbfp) considered a C++ API?
3. Next time onwards, how do I identify whether I am using a library or an API?

Thanks!

P.S: I understand my instructor can let me know whether we can use STL, but I wanted to know the difference between the libraries and the APIs irrespective of his answer; hence the question.