What is a trojan? What is a worm?
A trojan is a malicious program that masquerades as a legitimate application. Unlike viruses, they do not self replicate, but instead, their primary purpose is (usually) to allow an attacker remote access to your computer or its resources. Sometimes, users can be tricked into downloading and installing trojans onto their own computers, but more commonly, trojans are installed by an intruder to allow him future access to your box.
Trojans often come packaged as "root kits". A "root kit" is a set of trojaned system applications to help mask a compromise and facilitate unauthorized remote access. A root kit will usually include trojaned versions of ps, getty, passwd, tcp_wrappers, login, and syslogd.
A worm is a self-replicating, auto infecting program that spreads through computer networks. Unlike a virus, a worm does not require user intervention to be activated. Worms take advantage of vulnerabilities to propagate themselves across networks. Once it has infected a machine, a worm may also install a DDOS zombie, a r00tkit to prevent detection, or a trojan to allow unauthorized remote access. Many worms exist for Linux, including ADM, Ramen, and Lion.