Trojan is a program that usally is not what it seems. Usally designed to give remote access to a remote user. For exampel, You download the latest Macromedia Studio MX off of KaZAa and install it. It dosen't work or maybe it dose. But you also(unknown to you) installed a trojan horse program. Some script kiddie has just gotten complete access to your computer.
He can do stuff like open windows on your box, open the CD rom, Get into the BIOS, the list gose on....
A worm is a program that is self spreading. Usally an email attachment that will look at your address book when executed and emil it's self out to everyone on it. There are others however that do not need you to do anything to infect your box. It just gets in through your connection to the net, searches for a vunerability and infects your machine. Then uses your machine to launch out and attack or infect other machines. There are some kinda "Good worms" however too.
One nasty worm was "Code Red". Well a white hat hacker wrote a worm called code Green. This sought out systems infected with code red and then infected them with it's self. It would then remove code red and look for more systems infected.
This is still bad because the worm moving through the internet or network causes congestion. This can lead to lost, slow and or corrupted data.
Oh, Never heard of a honey net