By definition, a domain name is simply a human readable form of an IP address. In function it is the destination that you type into a web browser in order to visit a website, such a www.google.com. Metaphorically, it is very similar to how you would scroll to a contact in your cell phone rather than manually dialing the person by entering their full phone number; the phone number would be an IP address and the saved contact would be a domain name. Always buy a domain with a reputable domain registrar.
Web services are almost like normal a web page. The difference is that they are formatted to make it very easy for a program to pull data from the page, to the point of probably not using any HTML. They generally also are more reliable as to the consistency of the format, may use a different formal process to define the content such soap or raw xml, and there is often also a descriptor document that formally defines the structure for the data.
Unlike traditional client/server models, such as a Web server/Web page system, Web services do not provide the user with a GUI. Web services instead share business logic, data and processes through a programmatic interface across a network. The applications interface, not the users. Developers can then add the Web service to a GUI (such as a Web page or an executable program) to offer specific functionality to users.