When Web services use REST architecture, they are called RESTful APIs (Application Programming Interfaces) or REST APIs.

Representational state transfer (REST) or RESTful Web services are one way of providing interoperability between computer systems on the Internet.

REST-compliant Web services allow requesting systems to access and manipulate textual representations of Web resources using a uniform and predefined set of stateless operations.
Other forms of Web service exist, which expose their own arbitrary sets of operations such as WSDL and SOAP.

References:

Rest-api Wiki

Rest-Api