No it is not clear when to apply the MEL or the Abnormal checklist, but it used to be clear (up to approx 15 years ago).
The MEL should be applied up until setting takeoff power if you have failures on startup/taxi, and when airborne you look into the Abnormal checklist. That is the way we used to do it.
Let me give an example why : on taxi out you have an ECAM warning, and this failure is a “NO DISPATCH” according to the MEL. Common sense would be not to continue the flight, but as it is company procedure in many places, it is up to captain to decide if it is OK to continue (after using “good airmanship etc”.
In todays complex aircraft it should not be up to the captain to decide that. The MEL should be used/applied up to setting takeoff power.
Please give examples on in which European companies is the MEL used/applied that way (up to setting takeoff power) ?