ASP.NET Web services was developed for building applications that send and receive messages by using the Simple Object Access Protocol (SOAP) over HTTP.
WCF is for enabling .NET Framework applications to exchange messages with other software entities. SOAP is used by default, but the messages can be in any format, and conveyed by using any transport protocol.
You can view ASP.NET web services as a subset of WCF services.
Here is a link comparing the two frameworks.