Most viruses just replicate, a lot also do damage.
A program that makes copies of itself, for example from one disk drive to another, or by copying itself using email or some other transport mechanism. It may do damage and comprimise the security of the computer. It may arrive in the form of a joke program or software of some sort. Trojan A program that neither replicates or copies itself, but does damage or compromises the security of the computer. Typically it relies on someone emailing it to you, it does not email itself, it may arrive in the form of a joke program or software of some sort.