This thread is about web or network service APIs, which, thanks to the CFAA, have broad leeway to dictate what client software you are legally allowed to use to speak to it. It's a grey area and some real bullshit, IMO.

You are talking about programmatic APIs, which is a horse of a different color: a copyright issue, which is still being figured out.

It's annoying that we overload the same term for both things.