What people today call a router when referring to a device bought to share a broadband connection, is what is properly called a network address translator (NAT). It translates between “fake” internal network address and real public address. Routers use the Router Information Protocal to share with each other information about which networks are connected to them - that is, to which networks they can route your packets. If you are behind a “real” router, you have a “real” IP address on your NIC which you can give to anyone and they can reach your computer. If I gave you my internal IP address, you’d never reach me…you need the address held by my NAT.
Some people discuss the “firewall” feature of a NAT as though it is a feature…a NAT is not really a firewall - there is no way to get to the inside of an internal network without doing a port assignment. A real firewall sits somewhere between your computer and the router and filters out packets it doesn’t want to reach you.
Same thing with hubs. Today you probably cannot by an unswitched “hub”. But I’d call it a switch unless there is a shared medium through which all packets were sent to all nodes (regardless of if they wanted to listen) and collision detection is necessary to determine if two devices transmit over the shared medium at the same time.
Now we call it a hub if it doesn’t NAT, and a router if it does. No one owns a true router in their own home. Since all of these terms and concepts are foreign to new home networkers, why did they get started using the wrong ones? I don’t guess it is very important, but something I wondered about after seeing another thread.