A trojan, sometimes referred to as a trojan horse, is non-self-replicating malware that appears to perform a desirable function for the user but instead facilitates unauthorized access to the user’s computer system. The term is derived from the trojan horse story in greek mythology.
A computer virus is a computer program that can copy itself and infact a computer. A true virus can only spread from one computer to another.
The chief difference between a trojan horse and a virus is that a trojan horse does not replicate itself. A virus does.