LAN, wait a second!

So I set up a LAN between my desktop PC and my laptop via LAN cable but eventually I noticed that it worked even when the cable wasn't connected, you know, because both of them have wireless internet antennas. It took some time to realize as they looked to be about the same speeds, but actually aren't (54Mbps and 100Mbps). So maybe I don't even need the cable after all, it's borrowed anyway.

So I was wondering, when I send stuff between computers I'm not using my internet downloads/uploads, right? Right?

can i just get the modem cable and plug it in the network card on my desktop pc and then plug the other end in my laptop? the cable fits but i cant see the laptop or the pc in network places what am i doing wrong? inb4 30000 elitist twats no doubt