Then this must be different from all other cards that say to set aside "on this" or "under this"?
Why? Is there another card for which it doesn't make sense to say that "on this" is its own zone?
In a zone like the Native Village mat, or the trash pile, or Quartmaster, the cards are interchangeable. On the other hand, abilities that set aside cards, set them aside separately from other such abilities. Each creates a different zone. When you Throne Haven, the two cards get set aside in different zones. This is clear with Archive; although it doesn't say "on this" (yet), it works exactly the same way as Haven. If Crypt were Thronable (which is perfectly possible with a theoretical Night Throne) it would certainly create two different, non-interchangeable zones like Archive.
These cards are technically
set aside, meaning outside your play area. ("On this" and "under this" must have been added just as reminders, not because set aside cards technically are on or under the cards in play - which I think is confusing for abilities that care about cards in play.)
You can't claim that "set-aside land" is one zone either, because then Quartermaster would set aside cards in the same zone as Haven, so Quartermaster's zone wouldn't be distinct, so it would be impossible for a Throned Quartermaster to work the way the rulebooks says.