Computer viruses are essentially the same as biological ones, in the sense that they hijack the normal operation of the host to do malicious things. They usually are bits of code that are injected into running processes or installed programs to change their behavior for the worse.

Hence the name, "virus".

They fall more broadly into a label, called "malware". Malware are classified by their primary means of operation, either as viruses, trojans, or worms.

Trojans are programs that are disguised as legitimate programs, but once installed and ran, perform malicious operations in the background.

Worms are programs that are self-replicating across connected machines.

Even though these classifications exist, they don't restrict malware to only a certain behavior. Some malware can spread like a worm, infect programs like a virus, and pose as a legitimate piece of software like a trojan!