does a switchbox and a router serve the same purpose?

Answer 1

There are a lot of routers now that also act as switches as well, so yes they can serve the same purpose. However, a switch is not a router.

Answer 2

A switchbox is only useful in specialized situations. It's not useful in the same ways a router is.

You'd use a switchbox when you have multiple computers, but only want to plug one screen and one keyboard into them. So, you might use a switchbox in a data center, where you have a whole bunch of servers which you rarely poke at, and just need a screen and keyboard every now and then. http://en.wikipedia.org/wiki/Switchbox

You'd use a router when you want to route traffic, or need a piece of network equipment which is smart enough to understand IP addresses. Usually you buy a router to share your internet connection between a few computers (technically, you need a modem, a router, and a switch).

You might be curious about a switch, which is a bit different from a switchbox. You'd use a switch to connect multiple computers together. They're not very smart, but they're fast. Usually, you'll use switches to connect together all the computers in your building, and you'll plug the biggest one into a router, so all of the computers can get online.