Most of content in this post from Microsoft and related websites:
Firstly, we start from the simplest thing: The relationship of WCF Web API and ASP.NET Web API is WCF Web API is now “merged” to ASP.NET Web API, "ASP.NET Web API is effectively the next version of WCF Web API. There will not be a separate release for WCF Web API and we will retire all WCF Web API content by the end of 2012" :
Announcement: WCF Web API is now ASP.NET Web API! ASP.NET Web API released with ASP.NET MVC 4 Beta. The WCF Web API and WCF support for jQuery content on this site wll removed by the end of 2012.
(from WCF project)
We are happy to announce that ASP.NET Web API has now shipped with ASP.NET MVC 4 Beta!
ASP.NET Web API represents the joint efforts of the WCF and ASP.NET teams to create an integrated web API framework. You can get the bits and find articles, tutorials, samples and videos on the new ASP.NET Web API home page. We have also setup a Web API forum on the ASP.NET site where we will monitor customer questions and discussions.
What is WCF Web API ?
WCF Web API allows developers to expose their applications, data and services to the web directly over HTTP. This allows developers to fully harness the richness of the HTTP as an application layer protocol. Applications can communicate with a very broad set of clients whether they be browsers, mobile devices, desktop applications or other backend services.
What is ASP.NET Web API ?
ASP.NET Web API is a framework for building and consuming HTTP services that can reach a broad range of clients including browsers and mobile devices. It’s also a great platform for building RESTful services. ASP.NET Web API takes the best features from WCF Web API and merges them with the best features from MVC.
There is very important information which you might recognize something you need:
Why change the name? Web APIs have a foot in two worlds: the world of service orientation and the World Wide Web. We decided to align ASP.NET Web API with the rest of the Microsoft web platform, so we went with the brand that communicates this alignment. From a technical perspective we also decided to go with a new HTTP specific dispatcher instead of trying to carry forward the WCF dispatcher, so there is virtually no WCF code in the new stack.
About more information between WCF and ASP.NET Web API, Ido Flatow has a very good article here: WCF or ASP.NET Web APIs? My two cents on the subject:
What is the purpose of the WebAPIs?
When WCF was conceived back in its Indigo and .NET 3 days, the main goal was to support SOAP + WS-* over a wide variety of transports. However, over time it became clear that although SOAP is wide spread and supported on many platforms, it is not the only way to go when creating services. There is also a need to also support non-SOAP services, especially over HTTP, where you can harness the power of the HTTP protocol to create HTTP services: services that are activated by simple GET requests, or by passing plain XML over POST, and respond with non-SOAP content such as plain XML, a JSON string, or any other content that can be used by the consumer. Support for non-SOAP services was very much needed in WCF back then, mostly because some clients, such as web browsers, were not that suitable to handle SOAP messages (plenty of XML parsing and DOM manipulation).
About detail content, Please read above all articles which I provided Links.