Yes, if you want two separate, unrelated web sites they must be configured to use different directories for their document root.
Once you have a domain registered, you add hosting for it by using the Domains -> Manage Domains section of the DreamHost Web Panel. You can add as many domains as you like, you only have to pay for registration.
Keep in mind that if you are hosting a site for someone else, or try to share managing a site, its best to add a new group and user for each site and share credentials as necessary. When you add a domain, you pick one user that can be used to login and manage the files for the site.
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