Can someone please explain to me how a gateway differs from a router?

A gateway is the portal out to somewhere else, usually out of your local network to the public network, (the internet). A router can do this, but is more used to direct traffic between different networks, usually sub-nets on a private network. Example; I have 5 sub-nets all private behind a firewall. All 5 sub-nets are in different states, to print a report to a printer in another state a device has to know that the printer is not here, hence the router has information on how to "find" that printer since it's not local. The gateway serves all the sub-nets, anyone who wants to browse the internet or get email has to be able to go "outside" our private network, so the gateway sees this request and sends it out.

Well, sort of. A gateway can be used in many differe contexts. A gateway can be a 'translator' as in Gateway Services for Netware which will allow connection to a Netware server without any client software on the client initiating the connection. In your case, I think you might be referring to gateway in the context of Default Gateway. In this case, the term gateway refers to the interface of the router that will allow access out of your network. This is close to the post above. The router may have several ports that all go to different networks. So on network 1 you would configure the default gateway to point to the interface on the router that is connected to network 1. Any traffic from network 1 that is directed to another network would go to the default gateway and then get routed to the appropriate network - which is the job of the router.

Was trying to paint a broad picture since the question was also very broad. Hence the "portal" analogy, portal to Netware server, portal to IBM mainframe, portal to the internet, etc. Most people don't use the router to do the gateway work since nowdays the gateway, (yes the Default Gateway to the internet,{which is what 95% of people mean when they say gateway,[at least the ones I know]}), also needs strong anti-virus/filtering/firewall/anti-spam software, etc.

Usually, when you hear the terms gateway and router in the TCP/IP world they mean the same thing, aznluvsmc. It's is just a device that will route traffic from one network to another network. This can be between private networks such as business have linking one another or it can be between a private and a public network, such as between your pc and the internet. Depending on which one it is, will decide whether you need all the different types of filters (ie, firewalls, virus protection, anti-spam, etc.). What context was the term gateway used in that you are asking about?