Can anyone help me in giving the difference between API and Web service in Salesforce ?
A webservice is a service that is accessed over the web.
An API is a collection of ways of interacting with software components.
As examples in Salesforce specifically:
The built-in classes and interfaces that make up Apex are a collection of features that can be considered an API, but are not considered webservices since they are not accessed directly through the web. That being said, the Salesforce documentation typically does not use the term API when referring to Apex features, except when referring to code api versions.