What is the difference between en-route delays and airport delays?
The delays you mentioned are imposed by Eurocontrol to manage traffic flow all over Europe:


  Even when an aircraft is ready to depart, it may still be delayed by ‘flow management’ (ATFM). You may well hear that your flight is ‘waiting for its Air Traffic Control slot’ and this is explained in another article. In short, if there is a problem that will delay an aircraft either en-route or on the approach to the destination airport, then it’s safer and cheaper to hold the aircraft on the ground, not burning fuel, and give it a delayed take-off time.
  
  EUROCONTROL as Network Manager looks at all the flight plans and identifies where and when there are too many flights/too little capacity. This might be as a result of a peak in demand (aviation has rush hours too!), weather problems, limited capacity at the destination airport or many other possibilities. In total, flow management delays account for about 16% of total delays (in 2017), mostly relating to issues at the destination airport.


(Eurocontrol)


  ATFM departure slots are allocated centrally by the European Network Manager upon the request of the local Flow Management Position (FMP), when an imbalance between demand and capacity is foreseen at airports and/or en-route. The purpose of such regulation is to hold aircraft on the ground.


(Eurocontrol ATFM Slot Adherence)

To the pilots, this comes as a so called CTOT (Calculated Take-Off Time):


  
  A time calculated and issued by the Central Flow Management unit, as a result of tactical slot allocation, at which a flight is expected to become airborne.
  An Air Traffic Flow &amp; Capacity Management (ATFCM) departure slot, forming part of an Air Traffic Control (ATC) clearance, which is issued to a flight affected by Network Management regulations. It is defined by a time and tolerance (-5 to +10 minutes) during which period the flight is expected to take-off.
  


(Eurocontrol ATM Lexicon)

For each of these delays, there is an associated Reference Location where the reason for the delay is located. This defines, which delay category applies:


En-route delay:


  
  Delay caused by regulation based on traffic volume which has a reference location classified as AS (Airspace) or SP (Special Point).
  ATFM delay caused by regulations applied by the CFMU at the request of the FMP to protect en-route ATC sectors from overload.
  


(Eurocontrol ATM Lexicon)
Airport Delay:


  Delay caused by regulation based on traffic volume which has a reference location classified as AZ (Aerodrome Zone) or AD (Aerodrome)


(Eurocontrol ATM Lexicon)


Examples for delaying a departure could be:


enroute weather does not allow to fly the filed route at the moment (En-route delay)
weather at destination is not expected to be good enough to land at the estimated arrival time (Airport delay)
there will be too many aircraft in one air traffic control sector (En-route delay)
there will be too many aircraft arriving at the destination airport at the same time (Airport delay)