Simple explanation
Trojan Horse (Very Dangerous)
A computer file designed to steal personal data and details. These install themselves in memory so they can observe what is happening on your computer.
These files are the most dangerous as bank details and credit card details are stolen.
A good antivirus should detect and clean a Trojan, also deleting the file containing the trojan will work.
AVG Anti-virus will detect Trojan Horses (Free versions available)
Virus (Dangerous)
A computer program is designed to damage or destroy your computers or data. These install themselves into memory so they can infect other files.
A good antivirus should detect and clean a virus, however this does depend on how bad the infection is.
AVG Anti-virus is a very good anti-virus (Free versions available)
Spies (harmfull)
Small programs that create havoc on your computer. These embed themselves into the registry and load a file into memory
S&D Spybot is a very good spy removal program (Free Software)
A good spyware program will clean 90% of these files, however some spies require a specific program or routine to clear them.
( some spies are very difficult to remove).