Siteforce was the initial name of what is now Site.com. It was originally introduced as Siteforce, but then changed.
Site.com is a Content Management System (CMS) designed to allow non developers to implement websites by dragging and dropping different components on to pages and page templates. Data can be retrieved using data connection elements such as data repeaters or page data connections. Data can be submitted via forms that are backed by a custom object. The data connections are limited to single objects or simple relationships (nested repeaters to get children, parent lookups, etc.). There is no SOQL, Apex, or Visualforce.
Additionally, Site.com provides a mechanisms to grant different users different roles (i.e., some may only be able to supply content, some may not be able to publish). Once changes are made in Site.com they can be published at which point they'll be live.
Sites or Force.com Sites allows developers to create pages using Visualforce and Apex. More complex queries of the Salesforce.com data can be made. There is no CMS, outside of AppExchange apps, that is part of Sites.
You can have your own custom URLs with both Site.com and Sites. The help sections on Domain Management give an overview. The Adding a Domain help page has the specific steps to add the domain. You can do this by going to the setup menu, then Domain Management. After the domain has been added you can map to the site(s) from the setup Domain Management | Custom URL (see Adding a Custom URL help doc).