I think discussions like run the risk of often end up going around in circles. IMO, whether you call it LRH or ELRH, a list of criteria seems to be more important then a list of cartridges:
1. A cartridge that delivers sufficient energy/velocity for the target game with a well proven bullet capable of penetrating and effecting sufficient tissue/organ damage. I have personally found the 1800FPS/1000FP a good quideline for medium game. 1800FPS/1500FP for large game. Defining less then 1000 yards as LR and +1000 yards for ELRH also seems to be a good quideline for game hunting purposes. Developing a common language helps in discussions. The "shooters" may have different criteria or language.
2. A rifle capable of delivering first shot accuracy to within the vital zone of the target animal under well understood conditions.
3. A shooter well practiced with sufficient skills to execute 1 and 2 above. I compete, shoot, and hunt at long range. IMO, hunting success with live targets is far more difficult and complex, and rifle/cartridge compatibility with the individual is an important factor.