I find this question interesting because what I consider a long-distance walk or run has changed over the years. Five years ago, when I used to run regularly, anything beyond 5 km felt like a long-distance run. Nowadays, since I don’t run as often, even a 2 km run feels more or less long-distance.
So, for me today:
Long-distance walk: above 5 km
Long-distance run: around 2 km or a bit more :)
It really depends on one’s fitness level and recent habits, what felt short before can feel long later.