Prometheus can create alert based on Alerting Rules. Alerting rules are another form of Prometheus Recording Rules, which turn the results of the PromQL expressions into alerts that are sent to Alertmanager.
Alertmanager receives alerts from Prometheus and turns them into notifications (slack, email, pagerduty…) - note that alerts are configured in prometheus, not in alertmanager!
Alertmanager can aggregate related alerts, throttle alerts to reduce pager storms, mute alerts, and allows configuring different outputs for different teams. Its only job is sending a notification, human response should be managed by some other service or ticketing system.