Switches switch, routers route. More seriously, a switch connects multiple endpoints to form a network, while a router connects switches to create a network of networks, and it routes packets between nodes in the most efficient way so one side of a network can communicate with the other side of another network.

At home, some use additional switches to get more ethernet ports.

It's normally a switch and the question is reversed: what's the advantage of a router compared to a normal switch.

Routers extend switching capabilities for extra cost and some performance impact. It's a balance.

These terms aren't exact. A "layer 3" switch is a router.

Mostly the name is an indication of the intended purpose. Switches are nex to the edges of a network.

Having extra Ethernet ports on your single network

You could reuse a router but a switch will generally have better perf and theres less to configure or go wrong