If you have it in your head that a domain and Website are somehow the same thing or very nearly the same thing, reboot your brain now and start over. Your Internet memory has been corrupted and needs wiping clean for a fresh start.
Domains are used for giving names to computers on the Internet, so people
and computers have a way of referring to computers that they can both understand.
You didn't have to know that because people use names to refer to computers.
But what if there are two Nancy's in the office? Well, you could try nancy1 and nancy2, but why should the first Nancy have to rename her computer when another Nancy joins the company? So what to do? Aha! Why not tell the computers apart the same way we tell the Nancy's apart? We'll name Nancy Smith's computer nancy.smith and Nancy Jones' computer nancy.jones.
Guess what. We just invented domains. Domain names are just family names for computers. If computers really were named this way, smith and jones would be domains.
In real life, of course, the family names are much more likely to be the names of the companies. (Bosses have this habit of thinking they own the computers.) But their function is still the same. They let one company name its computers without worrying about how other companies name their computers.
Domains were originally called "name domains" - meaning domains (families)
of related names. That made the name of a name domain a "name domain's
name" - quickly shortened to just "domain's name" or simply "domain name".
If we had kept the original word order and still used "name domain", there'd
be a lot less confusion today.
There are many computers on the Internet that that do not run Web servers
but do have names in domains. Even the routers that shuffle packets around
on the Internet usually have such names. They aren't even computers in
the usual sense, and they certainly don't run Web servers, but they have
names in domains.
The system for doing these translations is DNS, the Domain Name Service, which is run by computers called nameservers. DNS resolves names into numbers. It also reverse-resolves numbers into names, so your computer can tell you the name of a computer it's talking to.
(DNS can do a little more too, such as indicate what computer handles mail for a domain.)
If your website is the only website on a computer, it doesn't matter whether you think of the name as applying to the computer or to the website. However, if your website is just one of the websites on a computer, then you had best understand how that affects the naming of your website before you get a domain name. See our page on Domains and The Web.