What's the difference between nat and pat?

Network Address Translation (NAT) and Port Address Translation (PAT) both map IP addresses on an internal network to IP addresses on an external network. Which method of address translation you use depends on the types of networks that you are translating and the number of available IP addresses that you have.

NAT (Network Address Translation) uses a pool of public addresses that are mapped one-to-one to the private (or "inside") addresses, keeping the port number intact.

PAT (Port Address Translation) uses a single outside public address and maps multiple inside addresses to it using different port numbers. That's why Cisco calls it "overload".