It is not a distinction without a difference, for the obvious reason that appreciation of land value goes to owners but not leaseholders.

Unless you can sell your lease for a profit, which is the impression I got talking to someone in this situation.

American land ownership is "fee simple", which is derived from English law, where the Crown ultimately owns all the land, but grants the landowner unconditional fiefdom over it. You don't actually own property, but rather certain limited legal rights over it, which is how they can get away with property taxes and eminent domain.