What is Router?
Router is device which connect two networks for example local network and internet. Routers determine whether the source and destination are on the same network or whether data must be transferred from one network type to another. Routers contain software called firmware for example it contains DHCP which provide IP address to all connected device. Router is also providing the facility of Switch or Hub. Router is also use as access point. For example, routers are commonly used in home networks to share a single Internet connection between multiple computers through cable or wirelessly through Wi-Fi.

What is Gateway?
Gateway is a network point that acts as an entrance to another network. When router routing the information from one network to another network then gateway specify the exits point and when any information is coming from another network then gateway is entry point. for example a device which is provide from ISP for internet service is a getaway which create exist and entry point to next network.