>So, $.ajax in JavaScript (jQuery) and cURL in PHP. That’s it.

This is a bit confusing. "That's it" makes it sound as though this is the complete scope of what people mean when they say API. Somewhere it should be made clear that we are talking about one API of a particular type.

After reading the post someone could come away with the idea that if you don't have .ajax and jQuery or cURL and PHP then you aren't using an API.