Not being a committed LD walker, as day walking suits my purpose better, but being fascinated by the concept of routes and how quality of way fits in with personal judgement of a route, I am rather intrigued by this.
I have walked across Wales a few times, a continuous walk along a planned route, over several days. Some years later on this forum a lady asked for advice on a route to walk with her son, how to walk across Wales and she chose the route I had taken, this apparently worked out very well for them but it is not a recognised LDP. So did they complete a long distance route or do a long distance walk. As previously said this seems arbitrary.
On another occasion I chose a strait line of around 90 miles with a fixed start point and and a specific destination point and tried to walk as close to the line as the terrain allowed.
This I did over several weeks hacking into the line I had discovered, using various means of transport. Again was long distance walking or creating a long distance route. I actually made some rather interesting discoveries along that trail, which rarely get raise by followers of recognised LD trails.