A Virus is software that will hurt your files or you system software. and copy it self to other peoples computers.

Spy-ware tracks the websites you visit ,,the software you have on your computer , copies everything you type . usually uploading it to a person . it can also to redirect you to websites.

there are a fantastic many others. Trojans, zombies etc etc

now most are just referred to as Mal-ware. ( for Malicious software)

To place it austerely…

Viruses are generally referring to something that can hurt your system; delete information, corrupt information, possibly slow your machine down… That type of thing. Trojans, which are generally a means to allow someone to infiltrate your system at will, are often built-in under the umbrella of viruses, but are really a point form of threat.

Spyware is something that gathers information on your computer. Cookies are most commonly the method used, where your browsing habits can be recorded. More serious uses can go as far as recording your personal information, and delivering this information at some later date. This can be used to target you for spam, and can be as perilous as exposing you to identity theft.

Both can be very perilous. Viruses are mostly targeted at your PC, but can do what Spyware does. Spyware is targeted at YOU.