WiFi and LAN set-up

I have a LAN network on which I have 3 computers, all working well together, sharing files and printers, connecting to the internet, etc. Two of the computers run Vista Home, and one (mine) runs Vista Ultimate x64.

I have a Linksys router which is also Wireless.

I just bought a netbook running Windows 7 Starter. I would like to be able to sync this netbook with my computer, the one running Vista Ultimate x64. Ideally, I would like NOT to have to plug the netbook into a cable, but rather to connect via WiFi.

Is it possible to set them up such that they can see each other? Someone told me that the LAN and WiFi are 2 separate networks and, thus, the 2 computers could never see each other... I kind of doubt it, because I can see the printers in both LAN and WiFi network, so --I am hoping-- logic would suggest that two computers could see each other, too....

Could someone help, please? Thank you.

Hello,
I have a desktop running Vista home premium 32 bit connected via ethernet to a netgear router. I also have a netbook running Windows 7 starter connected to the same router via wifi. The two computers can see and share files between them and share the internet connection and an HP computer as well. I'm not sure about the 64 bit thing, but i don't see any reason why it wouldn't work...
Hope that helps