Hi
Again this is a really big topic so it is pretty hard to put so much content into a small post
The simplest way to describe it is:
Published Application
This is when (To the user) the application seems to be running on their desktop, however it is actually being pushed from the server, they don't have access to the desktop of the terminal server, it is just pushing an application to them
Published Desktop
This is terminal services as most people know it, the user logs into the server and a new (server) desktop opens up, they can run programs on that server as they have been allowed to, you may decide to put some or all of the programs they use on the server and have them work in the terminal window, or they might only run some things and switch back to their local machines for some things
A full terminal server setup may have some users working on "Dumb" terminals (PC's with no local capability, they load up and directly into the terminal) and some users no whatever PC's the company still has
However everything is done on the server, they store their files there, run their applications, office email, everything, nothing is done on their desktop
This full terminal environment has great benefits if you have the server power to support all the users and the connectivity for the users to be able to work speedily
Cheers
Nev