Client in infrastructure or ad hoc mode
Assigning an IP address to your wireless interface is independent of the 802.11 network configuration and uses the same utilities or daemons as a wired network.
DHCP server on WAP acting as a gateway
If you've configured your WAP to act as a gateway, you will have your wireless network on a separate subnet from your wired network. In this case, you could be using infrastructure mode or ad hoc mode.