I have seen this problem only once before and it was due to the network being set up as thin client with bad settings. I am no expert on thin client and am speaking from an understanding of what others have explained.
Normally a Win 98 PC is set up with all the applications and data stored on each machine locally. Thus you have no interaction between the PCs.
When you have the PCs accessing data from a file server they are actually working on the file from the file server and not locally.
It is possible to set up some applications so that they are used from a server and not locally, this is a common situation with accounting software.
EG Server A has an application, PC B accesses and uses that application by having the commands form their PC sent across the network to the server and the operation takes place on ther server. When PC C logs on and works on that same program it is also using the server and the server resources. Kind of like two people having keyboards on the one PC.
Generally this is NOT a problem with thin client set ups as the clients should be working in different sessions with different resources assigned, ie different parts of the RAM and HDD for temporary storage. But when they system is NOT set up right they may be sharing a common memory location or storage area. Thus the system has the latest 'copied' item available. It is likely that the system is just making the last 3 or 4 clipboard items available regardless of who saved them.
Sort of like two people trying to use the same desk to sort papers instead.
If your system was set up thin client you should know. But Wordpad is usually run locally as part of the operating system.
I can't even imagine how they got this happening with Wordpad unless they were both working off the same file on a remote file server, then it should not be affecting the clipboard.
