As author of the aforementioned article let me try to give you give you some practical (as opposed to contractual) definitions explaining the difference between them:
EW (early warning): – where either Party are obliged to notify a matter which COULD effect in simple terms either time, cost or quality. The idea is that these items can be discussed and either avoided or at least their impacts minimized going forward (clause 16.1)
Notified CE (compensation event): - where either Party (but more often than not will be by the Contractor) notifies that they believe an event to be a compensation event i.e. an event has occurred that is not the Contractor’s risk under their contract. They need to notify what the event is and why it is an event (i.e. which reason within 60.1 makes it a CE). If it is agreed that it is one only then will there be a request for a quotation from the Contractor.
Accepted /Implemented: If a Project Manager accepts a Contractor’s quote or they have made their own assessment, the conclusion of this process is called “implementation” (clause 65) where by the Project Manager confirms their agreement of both the cost effect and time effect (i.e. movement of Completion Date/Key Date/Sectional Completion).
Non-implemented CE: a compensation event that has been notified but not yet implemented (implemented meaning “agreed value/time” rather than a reference to whether the item has been done yet). The effects of these should be shown on the programme, but only affecting “planned Completion” rather than the Completion Date. Completion Date itself can only move out when that event is “implemented”.
I hope that clarifies.