A am a bit confused with routers and gateways.

From my understanding if a client needs to send a packet to another which is not in the same ip segment it sends the packet to the gateway, behind which usually a router takes over. Is this somewhat correct?

But if thats the case, what do I need the gateway for? Or is gateway just a term to describe the default router (I know (or think) that a gateway can also be used to translate between something like ethernet and fiber)? Could I just plug one (or more) routers into a network without specefying a gateway?