I'm not sure if this is what you mean or not but: If I login as dale and start Mozilla then login again and start something say, top, for instance. Root can kill either, but from my understanding, which may be wrong, the first dale owns Mozilla and the second dale does not. The first dale can kill Mozilla because that dale started it. The first dale can not kill top that was started by the second dale because he did not start that program and does not 'own' it.
Since you may be new to Linux, security and stability are about the first things on the list. What you start, that specific user owns it, as in the one that actually started the process not the user name.
The same is not true when you generate a file though. Either of the dale's above can create a file and both dale's own the file. Same user. We used to run into this back in the Unix days. If you login to two terminals and one has locked up for some reason, you can't just kill the user, you have to kill the terminal, to make sure you get the right one, unless you want both to be killed.
I hope that makes since. The best way to kill a process, in my opinion, is to su and do it as root. Pretty much does the deed then regardless.
Hope that helps and is correct. If not some better guru may come along and correct or explain it better.
