What's the difference between web service and api

An API (Application Programming Interface) is the means by which third parties can write code that interfaces with other code. A Web Service is a type of API, one that almost always operates over HTTP (though some, like SOAP, can use alternate transports, like SMTP). The official W3C definition mentions that Web Services don't necessarily use HTTP, but this is almost always the case and is usually assumed unless mentioned otherwise.

For examples of web services specifically, see SOAP, REST, and XML-RPC. For an example of another type of API, one written in C for use on a local machine, see the Linux Kernel API.

As far as the protocol goes, a Web service API almost always uses HTTP (hence the Web part), and definitely involves communication over a network. APIs in general can use any means of communication they wish. The Linux kernel API, for example, uses Interrupts to invoke the system calls that comprise its API for calls from user space.