Sharepoint - What's the difference between Sharepoint Workspace, Groove Workspace, and Shared Folders?

Different products (if you can call Shared Folder as such). Basically SharePoint Workspace is the new Groove (in Office 2007). The Windows Process is still named Groove if you peek in your processes.

Groove Workspaces allow secure collaboration workspaces between partners, with the condition of both have SharePoint workspace running.

Otherwise, Shared Folders cannot even be compared as the SharePoint workspace enables offline scenarios and syncronization with SharePoint Sites (not just workspaces) of various content (multiple types supported - Task, Calendar, most important Document Libraries).

Hope it helps