What is the difference between Kunoros, Hound of Athreos' graveyard abilities?
The difference would be that not every card was a spell before it entered the battlefield.


  112.1. A spell is a card on the stack. [...]


Spells are objects you put on the stack after casting them - normally from your hand, but occasionally from your graveyard, such as with Abandoned Sarcophagus. The second ability of Kunoros prevents that from happening.

Other cards, such as Emeria, the Sky Ruin, will put creature cards in play without ever putting them on the stack, meaning they will never exist as spells. Kuronos's second ability does not apply to the Sky Ruin, but the first ability does and prevents even this ability from being useful.

Note also that Kuronos's first ability does not prevent the Sky Ruin from casting cards from the graveyard, because it only explicitly defines that cards can't change from the graveyard to the battlefield zone.