Would differentiating a refueling stop from a layover be useful?
No. Landing and taking off from the same airport should be considered a layover if you didn't leave the post security area. Staying on the plane or going into the terminal doesn't really make much of a difference as far as I'm concerned.
Think of it this way. If you never left the aircraft, the
plane still made a layover at the intermediate airport.
I had one layover at ORD where I had to disembark because the crew was changing. I ended up boarding the same plane (different flight number) for my onward journey. Doing the "milk run" in southeast Alaska typically involves several layovers between SEA and ANC. For those, you typically stay on during the stops. 50 years ago, crossing the Pacific usually included several fuel stops. In NAN, staying on board was common, while HNL usually allowed getting out.
Airlines that don't operate a full hub and spoke model (Southwest and Breeze come to mind the US) might make several layovers potentially using the same flight number.
Best to keep it simple.
Here's my definition:
A and D require going into or out of the security area.
L would mean staying in the secure area (I would consider a layover that involved leaving the secure area as A + D rather than L, but that could be up for debate).
X would mean never crossing into the secure area.
Others may define things differently, but these guidelines should work for most