Trojan Horses vs. Viruses

I used to use the latest version of Norton Antivirus (2008), when I switched to Avira, because the former is slowing my computer down. To my surprise, Avira, which is a free anti-virus, has detected a total of 51 viruses and two trojan horses. Avira's disinfectant grade for trojan horses, however is not as good as its detection grade. While many viruses and few trojan horses were identified, Avira cannot actually remove the trojan horses.

Based on my understanding, a trojan horse is not really a virus. It is a destructive program disguising as a harmless and beneficial application. Below are the differences and similarities of trojan horses and viruses.

Trojan Horses vs. Viruses (Differences and Similarities)
Trojan Horses
1. Self-Replication - no
2. Malware - yes
3. Introduce More Viruses - yes
4. Take Advantage of Security Flaws - not necessary
5. Destructive - yes

Viruses
1. Self-Replication - yes
2. Malware - yes
3. Introduce More Viruses - yes
4. Take Advantage of Security Flaws - yes
5. Destructive - yes

The extent of destructiveness of trojan horses and viruses are the same. Both malwares execute commands without the user's knowledge and permission.

Two types of trojan horses were detected by Avira:

1) Application.Ardamax_Keylogger
Ardamax Keylogger is a keystroke recorder that captures user's activity and saves it to an encrypted log file. The log file can be viewed with the powerful Log Viewer; and,

2) Trojan.Agent.KQ
Trojan.Agent.KQ automatically runs from Windows startup and attempt to access bad sites in order to download more malware onto infected computers.

Unfortunately, Avira cannot get rid of the trojan horses... Oh my... I think, I have to try another antivirus...