Malware definition

Malware is a universal name for a piece of software injected into computer system to induce harm to that system or other systems, or to undermine them for use other than that proposed by their owners. Malware can get remote access control to information system, record and forward data from the controlled system to a third party without the users’ authorization or knowledge. Information systems which have been compromised are able to perform illegal security actions which can harm the information system, or otherwise affect the data and system integrity.
Viruses, worms, trojan horses, backdoors, keystroke loggers, rootkits or spyware and different types of malware are described in the next section. These terms correspond to the functionality and activities of the malware (e.g. a virus is self spreading, a worm is self replicating). Malware research analyst’s experts generally cluster malware into two classes: family and variant. “Family” refers to the distinct or original piece of malware; “variant” refers to a different version of the original malicious code.

So how do we differentiate between a computer virus and a worm? How are these different from Trojan horses?