Gianni,
As James says, whatever is connected and giving out IPs is your DHCP. If you have a peer-to-peer network, the router could still give out IPs. A computer with a DHCP server could give out IPs.
A domain basically takes a network and usually centralizes the data at the server. A domain is for handling permissions, resources and policies making use of DNS. Single authentication. Two computers on a domain are more likely to have access to each other, while two computers joined to a private network but not on a domain will likely not have access to each other unless one PC goes out of its way to provide permissions as would happen in a P2P.
Think of Starbucks. Starbucks provides Wi Fi access for its customers. It provides an IP address to wireless hardware and does not require a password, mainly because the wireless router is not connected to a network that would need to be protected. But, there is no domain there. Anyone else should not be able to access your device through the router unless the other person is 14 or under in which case, they could likely steal everything on your laptop in minutes.
