Server monitoring is the practice of collecting resource metrics from the machines that run your services and alerting when one of those resources approaches a limit. It answers questions about the host itself: is the CPU saturated, is memory leaking, is the disk filling, is one volume being hammered.
Server monitoring and uptime monitoring answer different questions, and neither replaces the other. An external HTTP check tells you within seconds that customers are affected, from outside your network, with no agent to trust. Host metrics tell you why, and usually show the problem building for hours first: available memory sliding down, free space shrinking at a steady rate, load average creeping past the core count. Run both, page primarily on the external check, and use the host timeline for diagnosis plus the slow burn conditions an external probe cannot see at all.
One piece teams routinely forget to configure: an agent that stops reporting is itself an incident. Hyperping marks metrics Stale and then Offline past a threshold, which opens an outage and fires the same escalation policy as a failed HTTP check, so a host that dies silently still wakes somebody up. Server alerting on resource thresholds is available on the paid plans.