I think she wanted to know the difference because she posted 2 similar definitions that absolutely wrong...
A Router is a device that routes information... it contains all the information needed to do NAT... basically it handles non-routable IPs, and NAT allows the real IP on the outside of the network to be shared with as many computers as possible...
A switch has absolutely 100% no ability to do routing... unless... of course you have a very advanced switch, like a Cisco Catalyst, where you can get a card to do the routing... but by definition the catalyst is a switch...
But typically, unless you are very smart, and work with very expensive technology.... a router does the routing and security, and the switch does all of connections... Switch is direct port to port.... where a HUB actually broadcasts all data across all ports... which allows for easy data sniffing...
But usually a router will have like 1-6 ports for various connections... like internet, serial, and a couple of internet ports...
A switch can have hundreds of ports... I have never heard of a router that has more than 10 ports...
Good luck