What is difference between distributed and time sharing computer?

Time sharing means that many users share a single computer. This was in the days of big mainframes and dumb terminals. It is an example of multitasking (many processes running on one processor). Time slice is one way that processors can multitask. This was the origin of client/server programming, many clients share the server.

Distributed computing is when a process running on one computer uses software modules running on many other computers. The Seti-At-Home screensaver is an example of distributed computing. The screensaver running on your computer calculates a small set of all the data collected by Seti when you processor is idle. The main computer collects all the analysed data from thousands of running screensavers.

The following is about preemptive/non-preemptive multitasking. It is concerned with only one computer. In a time slicing computer, there is an algorithm that decides how much time on the processor each of the processors need. It can very this dynamically. If a certain process doesn't voluntarily give up it's control of the processor, the central time-slicing process can force it off the processor. Most operating systems use time-slicing. Unix, Linux, OS X, Windows XP, etc. all use it.

In a distributed/cooperative computer, each process has to willingly give up its control of the processor when it's done. If a process doesn't give up control, then the whole computer crashes. This is a lot less stable. Any Mac OS prior to OS X uses distributed processing.