Web Service in ASP.NET
A Web Service is programmable application logic accessible via standard Web protocols. One of these Web protocols is the Simple Object Access Protocol (SOAP). SOAP is a W3C submitted note (as of May 2000) that uses standards based technologies (XML for data description and HTTP for transport) to encode and transmit application data.
Consumers of a Web Service do not need to know anything about the platform, object model, or programming language used to implement the service; they only need to understand how to send and receive SOAP messages (HTTP and XML).
WCF Service
Windows Communication Foundation (WCF) is a framework for building service-oriented applications. Using WCF, you can send data as asynchronous messages from one service endpoint to another. A service endpoint can be part of a continuously available service hosted by IIS, or it can be a service hosted in an application. An endpoint can be a client of a service that requests data from a service endpoint. The messages can be as simple as a single character or word sent as XML, or as complex as a stream of binary data.