Trojan Horse is a malware (malicious software/program) that can take over control of your machine. Trojan begins its action once it has been installed on the machine. With Trojan, hackers can have access to spy on a machine on which the Trojan has been installed thereby enabling them unauthorized access to sensitive data on the machine. With Trojan, user data can be blocked, stolen and even deleted.
A virus is also a malicious program just like Trojan. But unlike Trojan, a virus will replicate itself by copying itself to other programs in the affected machine thereby modifying these programs.
Both Trojan Horse (or simply Trojan) and Virus are malicious programs. Also, whether or not malicious, they are both programs. So it's superfluous to say one is a malicious program and the other is just a program.
