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Basically, a switch is made to combine multiple computers and route them to the internet.
The most typical way to connect a computer to a switch, is by using the twisted pair cable also called ethernet cable.
A managed switch enables better control of networks and the data frames that move through them.
There are many functions you can do with a managed switch. For example you can block ports, manage all LAN-cables and so on. It depends, which switch you have, you can manage every setting on a web-browser.
An unmanaged switch is usually very uncomplicated, as it is simply a plug and play system. without an administrator and the ports are set automatically.
A router is used for internet access. A router is a switching device for networks, it routes network packets to other devices (computers…) or networks.
At home you'll probably have a router, which is usually delivered by your network provider.
They also offer you an installation service. If you have a little bit of IT knowledge, you could do it on your own.
Also, a router connects multiple IP networks.