Thanks, melloman. I think I may even understand all that!
I doubt I am using DHCP since the computers are networked through a hardware broadband router/print server. When I set them up, I used "winipcfg" to check that the static IP was in the range recognized by the router yadda yadda. To the best of my knowledge there is no host computer. If the router is on, either computer works with the Internet and if both are on, they are networked.
When I get a little more confidence, I think I will fiddle around with different sort of netowrking, just for fun. In the meantime, the inhouse LAN works and the kids are happy campers.
Mary