yes, each domain you host on DH is separate from the others.
However you do not need to transfer the registration from godaddy to host the website here at DH. There's two parts to having a domain. First is registration: you pay to reserve that name as yours. Next is hosting: you pay a host, such as DH, to store you files for you and serve them to visitors when they type in your domain.
If you want, all you have to do is log into godaddy and update your nameserver to point to DH: ns1.dreamhost.com ns2.dream... and ns3. Then add the domain here at Dreamhost through the panel > domains > Manage domains.
You can transfer your domain name to DH if you want, but there is no need to and several people use seperate hosts and registrars.
Each site that you host here at DH has a folder created to store website files in - a different folder for each and every domain. Each domain has separate E-mail address, and everything. (if you should want a domain to mirror a different one you can do that too)
Hope this helps to clear things up.
art.googlies.net - personal website