Lots of people are confused between router and gateway. For some this becomes especially confusing when the gateway is referred to as the gateway router. Often, the 2 are the same parts of equipment. The differences slouch in their functions within the network.

What is a router?
A router is a part of networking gear which routes traffic between networks or subnets. Routers function at layer three, meaning they route based on IP addresses.

Route Tables
Routers use route tables to find out how to route traffic. IP addresses or address ranges are allocated to every interface, and when a packet is routed, the target address is located in the table so the packet is forwarded out the right interface.

What is a gateway?
It is the connection from your network to the outer globe. All traffic not intended for a different subnet or part of the internal network is sent to the gateway and on to its external target.

Gateway route tables
The gateway router, like any other router, uses a route table. However, the wildcard or ALL address definition is used, signifying that all traffic not chosen as inner gets sent out into the outside world.