Functional and hierarchical type of escalations can often be found within the IT Service Managed environment when Incident and Problem Management disciplines are implemented.
With functional escalations the incident\problem is routed to a more experienced entity that can deliver the next level of support.
Hierarchical escalations on the other hand act more as a communications means to inform both support staff and management in a proactive manner of potential SLA (Service Level Agreements) breaches.
The two types of escalations are intertwined as management would often use hierarchical escalation communications to functionally escalate incidents and problems to more skilled support personnel. The type of request and its priority would determine the time fame in which these escalations would occur.