Proxy: Software which acts as an "intermediate" between a client PC and the web server. Normally caches pages, which means it can serve them up quicker to client machines.
Gateway: A host which is the "default route" out of a network to another network. Often this is the router.
Router: An OSI model layer 3 device, which deals with logical addressing. It passes data between two networks with different logical addresses (such as IP addresses). Often used in SOHO installations to share an internet connection with a single public IP address to multiple PCs within a LAN (Local Area Network) using a method known as NAT (Network Address Translation)
Some may be wrong/not complete, I'm sure someone more knowledgeable will be along soon to correct me
Confused