API: Application Programming Interface “An API is a set of definitions and protocols for building and integrating application software.”
REST API: “Representational State Transfer API”
API is basically a set of functions and procedures that allow one application to access the features of other applications, REST is an architectural style for networking applications on the web. It is limited to client-server based applications. REST is a set of rules or guidelines to build a web API.
There are many ways to build a web API, and REST is a standard way that will help in building it faster and also for third-parties to understand it better.