ASP.NET MVC excels at accepting form data and generating HTML. It returns Views and Data. Requests are mapped to action names. MVC features exists in the System.Web.MVC assembly.
ASP.NET Web API excels at accepting and generating structured data like JSON and XML. It returns only Data not View. Build Restful services and supports content type negotiation (response data format can be JSON, XML, ATOM etc). Requests are mapped to actions based on HTTP Verbs. With the Web API, no longer IIS need to be used to host HTTP services, services can be hosted in a custom Windows service, console application, or any other type of host you need. Provides automatic support for OData. The model binding, filters, routing and others MVC features exist in Web API are different from MVC and exists in the new System.Web.Http assembly. Light weight architecture and good for devices like smart phones.