Which type of malware spreads from one system to another or from one network to another and causes similar types of damage as viruses do to the infected system?

Worms are self-replicating malware that spread autonomously across networks and systems by exploiting vulnerabilities or using network services, consuming resources, and causing damage, which aligns perfectly with the question's description.

A rootkit is a stealthy collection of tools designed to maintain privileged access to a system while hiding its presence, not primarily for self-replication across networks.

Adware is software primarily designed to display advertisements, not to self-replicate or cause system-wide damage comparable to a virus.

A Trojan horse is malware disguised as legitimate software that relies on user execution to infiltrate a system and does not self-replicate like a worm.