This is somewhat a tricky question to answer. Typically the anti-virus companies attach their own label to a malicious file, be it a virus, a trojan, a downloader, a file infecter, a rootkit, a backdoor. The names and how they are defined are up for grabs, there is no standard that I know of. The definitions aren't as clear cut as they used to be. And add to that mix the slew of malware, adware, spyware and so on...Virus according to Microsoft:
Computer viruses are small software programs that are designed to spread from one computer to another and to interfere with computer operation.
A virus might corrupt or delete data on your computer, use your e-mail program to spread itself to other computers, or even erase everything on your hard disk.
As you can see the main purpose of a virus is to cause harm and spread. There are several types of viruses, but they all have that same goal. Disrupting the normal activities of the computer it infects.
A trojan is more insidious. It tries to avoid detection. The name actually says a lot. It will try to confuse the system into thinking it is something else. But again, the goal is to disrupt. Or to gain access to install another type of nasty. They often allow remote access.A couple of
informative links on trojans.
Worms are like viruses but their initial purpose is to replicate, more than do damage. They can replicate so fast, they will slow your computer down to a crawl in a matter of minutes. They also actively seek out exploitable computers on the network or over the internet to spread to thus bogging down the bandwidth. Making your surfing practically impossible at times.
And those three are just the main ones. They are the least of our worries now. The problem now with the definitions, is that the writers of these programs don't stick to one kind of behaviour. So you can have a trojan with virus like functions. You can have a worm that's also a rootkit. You can have a backdoor that also sends spam through your email. And they all have shown they can annoy the user with popups, redirects and so on.
Bottom line is, the definitions are to be taken with a grain of salt. The main thing to remember is that you don't want either of those on your PC. So keeping safe practices, and making sure you scan often with your security programs and get the occasional second opinion from an online scanner, is really the best way to protect yourself.Best Practices - Internet Safety For 2008Antivirus, Antimalware, And Antispyware Resources
The above links are recommended reading to everyone.