Aside from extra hardware, routers generally have a firewall built-in and can perform NAT translations and otherwise act as a gateway. They do DHCP in most cases, too. Of course when you start to look at enterprise setups things get a little more complicated.

Since routers act as gateways, they have their own IP address too.

Switches are not gateways. They join two physical segments and mask them as a single logical segment. They do routing only in the most basic of senses - moving packets between the physical lines.