Process fault (pattern) will invoke check faults (aka health checks) on influencing entities while triaging. If the required blueprint topology is present health checks will get invoked.
Health check is slightly separate use case, it is purely checking and detecting faults. So you can trigger it on-demand or schedule it. Whereas Process fault is in response to an issue attempting to triage/resolve it.
If you want to resolve a fault that is detected during HC, you can configure it by setting the “Fault Triage policy”