Dhcp would be your local PC IP, your wan IP is given by the DNS server.
It's still DHCP, just from the modem to the router. In some cases, usually DSL and in all cases where you asked for a static IP from your ISP, you'd have an IP assigned to you directly, that that is still not a DNS function.
DNS just maps your IP to a "real" name, it does not assign that IP to you.
The ISP has a DHCP server that they use, same as the one in the router. When you use a "release" or a "renew" command on the router's WAN port, it the same as giving your PC a "ipconfig /release or /renew" command. The modem actually acts as the DHCP server for your WAN port, and the modem gets it's configuration probably from a static IP that is setup for it so they can track and support the modem you have.