I'm not sure what you mean by normal Rest.
REST is a paradigm.
HTTP is the protocol following this paradigm.
The ASP.NET Web API allows developers to write ASP.NET applications that can be accessed through HTTP and adhere to the REST paradigm. Although you can create a REST API without a Web API, the Web API provides a ton of features that can eliminate the big pain associated with creating a truly RESTful API in ASP.NET.
apigee REST API.