Difference between Web Services and Web APIs:

Web services are a type of API, which must be accessed through a network connection. APIs are application interfaces, implying that one application can communicate with another application in a standardized manner.
Web service is used for REST, SOAP and XML-RPC for communication. API is used for any style of communication.
All Web services are APIs. APIs are not web services.
It doesn’t have lightweight design, needs a SOAP convention to send or receive data over the system. It has a light-weight architecture furthermore, useful for gadgets which have constrained transmission capacity like smart phones.
It provides supports only for the HTTP protocol. It provides support for the HTTP/s protocol: URL Request/Response Headers, and so on.
It is not open source, however, can be devoured by any customer that comprehends xml. It is an open source and also ships with .NET framework.
Web service supports only XML. API supports XML and JSON.
Web Services can be hosted on IIS. Web API can be hosted only on IIS and self.