Missing from the current answers is
- DHCP is a protocol for configuring hosts, and runs periodically to keep their addresses and other configuration up to date. The traffic is between the host and a DHCP server; typically both are on the same local network, but not always.
- NAT a process is for rewriting packets as they are forwarded across a router. Specifically it translates the addresses and sometimes the ports. The traffic is across a router, typically between an ISP and its client, or between two organisations.