You're really comparing apples and oranges. A web service is simply a program that you can "call" using the HTTP protocol. Typically, HTTP requests sent to the service contain some XML describing the method called and any parameters. The response from the service likewise contains XML with the return value and any output parameters. It's a little more complicated than this, but it gives you the basic idea.
Windows Communication Foundation (WCF) is a framework for building network services. You can use this framework to build web services if you wish. I suspect that what's tripping you up are the various Visual Studio project templates. You have one for WCF services and one for web services. The web service template builds a web service that runs inside of IIS. The WCF template gives you far more flexibility (you can make a web service as a stand-alone application, for example), but it is far more complicated.
If you're just beginning, I'd start with web service template and IIS-based web services.