The only thing I know is that virus can get into the other programs and infect it whereas worms cannot attach itself to another program.
2 Answers
A virus, by its original definition, is a piece of code that gets attached to other programs. An executable gets "infected" and still works more or less as normal but also executes the virus payload when it runs, typically infecting other programs on the same computer. True viruses are rare these days.
A worm is a program that replicates itself over a network, generally by exploiting a vulnerability in some application.
Finally, a Trojan is a program that gets delivered to a victim which the victim must manually run on his own, often because he thinks it's something else.
The word "virus" is frequently used to refer to all three of these types of malware, though technically it only applies to the first.
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Worms travel from computer to computer on their own. Effectively they have the ability to hack remote computers (internet and intranet) to get into other systems. Viruses are more localized, meaning they travel from program to program. Viruses tend to be given to other computers by nature of infecting a program and that program is transferred to another computer with the virus included within that program. Human interaction is generally required in other words.
Maybe this page will help: The Difference Between a Computer Virus, Worm and Trojan Horse http://www.webopedia.com/DidYouKnow/Internet/virus.asp
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1There are many hybrids that do combinations of things (like a worm that also has the ability to act as a virus, or even a trojan that allows other people to break into your pc...) – Jeff Clayton Aug 14 '14 at 14:19