Except the term "web service" is just as overloaded as "API" - its got the very specific old school meaning of a SOAP/WSDL API which typically isn't exposed as a service on the web :(
Alas, that seems to have also been reduced to simply meaning "JSON over HTTP", instead of taking advantage of Hypermedia, but there is hope with more articles, such as http://www.infoq.com/articles/programming-semantic-profiles, being written.