Hi
When you log in to a computer on a network, and you start disk cleanup or defragmenter or any other system tool from your Start>Programs>Accessories menu you are accessing programs 'locally' and are telling them to work on the 'local' machine. 'Local' refers to the computer you are sat at. So these commands will only affect the computer you are starting them from.
You may have read about remote management and terminal services - these create user environments which are started from a local PC and which then connect to a server or a networked PC and usually require a password. So it should be obvious if you are connected to a remote machine. Also, the window will usually tell you it is connected to \\xxxx.
When running 'local' programs they usually say they are working on Drive C, which is the default letter assigned to the local hard drive that contains the OS.
Do not hesitate to post any other questions/comments. There are a lot of folks here who have a lot of good advice.
Hope this helps