in what scenario would you use a switch instead of a router
The router is generally provided to you by your internet service provider. It is the device which assigns IP addresses to your local computers/tablets/phones, and it is the box which is the gateway to the internet. To add more devices to a network, you don't mess with the router, but instead add a switch. Or possibly, you add a special box which acts as a wireless access point, which allows wireless devices to reach the router (and hence the internet). Once things can reach the router, the router can connect them to the internet.