I have been asked about the difference between Web API and RESTful services and that is also an interesting question to me. From my point of view, the only possible difference between RESTful service and Web API can be considered as that RESTful services are inherently meant to be stateless (although we can use cookies), while the concept of being inherently stateless does not apply to Web APIs as we can use sessions (can't be used in RESTful service).
However, I decided to post this question to see if there are any other potential differences that distinguish these two technologies from one another.