Two users logged into one server remotely

Hi,
First of all-- please excuse any really stupid questions i ask here-- not that great on the networking Recently i logged into a server remotely from home through Remote Desktop onto a machine running Windows Server 2003. I noticed in the Users tab of Windows Security that there was another user logged in at the same time. Now, my question is, is that user confined to what i see and do (we see the same things and there is only one mouse) (sorry 4 not explaining that very well but i hope you get the picture) or does each person have a individual control over the computer?

Thanks for any help you can give, and please don't hesitate to ask any questions if i did not explain correctly.

Thanks,
Conmoy.