Which type of intrusion detection system can monitor and alert on attacks, but cannot stop them?

Detective is not a standard IDS classification - the recognized operational categories are passive and reactive (also called active).

A passive IDS operates by inspecting copies of network traffic out-of-band, logging events, and sending alerts to administrators without interfering with actual packet flow. Because it cannot insert itself into the traffic path, it is fundamentally incapable of blocking or stopping attacks in progress.

Intuitive is not a recognized IDS classification in any security framework or certification body's terminology.

A reactive IDS can actively respond to detected threats by taking countermeasures such as resetting TCP connections or reconfiguring firewall rules, meaning it CAN stop some attacks.