Short Answer
There is no difference, as long as the server the site is on allows both uses. For example, on my servers, I have a rule which says both using www and not using it are redirected to the domain without www (i.e., www.mysite.com will just automatically redirect to mysite.com).
Long(ish) answer
You might be wondering at the reason behind having www.
Basically, the domain name (i.e. the name of the server) is "my_site.com" or "my_site.org". In other words, the domain name is my_site, which gets translated to a specific server somewhere out there.
The thing is, domain names (and servers) have existed before the World Wide Web. One example of this is email: before there was such a thing as a "website", there was email (and message boards, chats, etc).
So when the World Wide Web came into existence, most servers were already in place and set up to do things like file transfers, email, etc. To differentiate between accessing the server for the purpose of visiting its website, and using the server for something else, the standard was to go to *www.*my_site.com.
Of course, nowadays, the Internet and the World Wide Web are pretty much the same thing (in the public's mind), so it's pretty standard for domains to work both with and without a "www" part.
Hope this helps clear up any confusion.