A Trojan horse is technically not a virus. Trojan horses get their name from ancient literature where Greeks pulled a great Wooden Horse infront of the gate of Troy. The Greeks were hiding in the Horse and when the Trojans pulled in the Trojan Horse. The Greeks came out at night and opened the gate to let their army in.
Trojan horse are mostly made to cause damage, but can also be harmless. They are classified based on how they breach and damage systems. The six main types of Trojan horse are:
Remote Accessing
Data Destruction
Downloader
Server Trojan(Proxy, FTP , IRC, Email, HTTP/HTTPS, etc.)
Security software disabler
Denial-of-service attack (DoS)
A Trojan horse does not replicate themselves as viruses do.