BEST DOMAINS

Most people are unaware that they use sub domains daily. The famous "www" of the World Wide Web is an example of a sub domain. Sub domains can be created on a DNS server, and they don't need to be registered with a domain name registrar, of course, the original domain name needs to be registered before a sub domain could be created.
Examples of sub domains used on the internet are http://store.apple.com and http://support.microsoft.com.
Sub domains can be requested from your web hosting provider.

False Domain Names - Directory Listings

Some providers will offer you a name under their own name, like:  www.theircompany.com/yourcompany/
This is not a real domain name, it is a directory - and you should try to avoid it.
Directory domains are not desirable, especially for companies.
Typically, directory domains are used for personal web sites and free web sites provided by an ISP, you may have seen www.theircompany.com/~username as an address.
Competition in domain name registration has resulted in a dramatic decrease in pricing, so domain sharing is not common, since it is possible to register a domain name for only $15 per year