I'm always confused by router and gateway. Are there any differences between these two?

I've installed 2 network card on my computer in which I've installed Redhat 7.3. I want to config it as a gateway or router so that I can connect it to the internet using eth0 and connect it to a subnet (hubs) using eth1. Are there any specifications on IP address such as the IP address of the computers in the subnet and the IP address of the gateway eth1???

Thanks in advance,
William