I got similarly confused, a little, when I upgraded from dialup to DSL. Because I now need an ethernet connection between my computer and my router-modem, I’m in effect on a one-station local network which in turn connects to the internet. The system now uses its onboard (Intel) network controller as part of the connection, rather than the internal modem.

My router has slots for 4 local connections … eventually I’ll get my wife’s computer, upstairs, hooked into it so she can have internet access too. Just how will be an interesting problem – because all walls and floors here have steel fire barriers, wireless is probably not an option, and a cable would have to zigzag so much that it would probably be pushing the limits of acceptable length.