If you are connecting the modem (more likely to be a router if it has wireless) directly to the PC via USB it will appear as an Ethernet card (ie 'Local Area Connection').
If you connect it via Ethernet (network cable) then you are seeing the Ethernet adapter already in your computer appearing in the XP connections list.
A wireless router can function as a basic access point to provide wireless connectivity to laptops or computers with a wireless card installed by simply ignoring its internet settings and leaving the internet port unplugged. This is how you would set it up if you want to create a wireless network around the house.
A few models of router can operate as a client to other wirelss networks by plugging the router into a PC via its Ethernet connection, although this is not very common.
The one thing a wireless router cannot do is function directly as a wireless network card; in either mode above the wireless settings can only be configured in the router itself so all you see on the PC is a normal network connection.
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