Well the main difference is one is an application installed on a users computer (ZD), while the other is installed on a server which people access over the web.
If that doesn't clear it up you can try something like this:
In the interface you should have a search bar at the top, type this into it
and it will pop up a dialog box.
For the server (ZWC) it will show something like this:
while the desktop will show this:
Client Version: 6.0.3_GA_1915.UBUNTU8_64
Client Release: 20091118125312
Build Date: 20091118-1302
Client Version: 0.0
Client Release: build
Build Date: 20090827-1659