When a card refers to itself it literally means that specific object only. For example, Caustic Hound‘s ability will only trigger if that specific Caustic Hound goes from the battlefield to the graveyard. If you have two in the battlefield and one goes to the graveyard, the ability of the one in play will not trigger.

There are a few abilities that refer to card with specific names, but in these instances it is very clear. For example, Relentless Rats‘s ability refers to cards with the same name as it. In fact in the first instance Relentless Rats ability refers to itself, in the second it refers to all other cards on the battlefield with the name Relentless Rats.