Many effects in Magic will cause a card or permanent to go from one zone to another. One of the most common way this happens is when a permanent in play is destroyed or a card is discarded and it goes to the graveyard. When a card goes from one zone to another it is treated as a new object, unless the effect that moved it is specifically looking for it in this new zone.

For example, Oblivion Ring will exile another nonland permanent in play with its enters the battlefield ability. Oblivion Ring has a second connected triggered ability that specifically refers to the exiled card. Because of this, the second ability will return the exiled card to play.

However there are tricks you can use with Oblivion Ring to exile a card permanently. If you remove the Oblivion Ring from play, with something like Disperse, before its enters the battlefield triggered ability resolves, then its leaves the battlefield trigger will end up going on the stack and resolving first. As this targeted nonland permanent has not been removed from the battlefield yet, it cannot be returned to play. Then when the initial triggered ability resolves the targeted permanent will be exiled. If this exact same Oblivion Ring card were to be played again, it is a new object. It will not have any connection to the nonland permanent that was exiled previously.