API's are a published interface which defines how component A communicates with component B.
For example, Doubleclick have a published Java API which allows users to interrogate the database tables to get information about their online advertising campaign.
e.g. call GetNumberClicks (user name)
To implement the API, you have to add the Doubleclick .jar file to your class path. The call is local.
A web service is a form of API where the interface is defined by means of a WSDL. This allows remote calling of an interface over HTTP.
If Doubleclick implemented their interface as a web service, they would use something like Axis2 running inside Tomcat.
The remote user would call the web service
e.g. call GetNumberClicksWebService (user name)
and the GetNumberClicksWebService service would call GetNumberClicks locally.
