For your information: the term NAT is often used to describe different techniques (to reach a similar goal). You could identify two basic types:

(Static) NAT, or Network Address Translation, lets you have a big pool of IPs (your internal network) connect to the outside network using smaller pool of IPs. You need an 'outside IP' for each simultanious outside connection.

Using PAT, or Port Address Translation (or NAPT, Network Address Port Translation), you let a pool of IPs (again, your internal network) connect to the outside network using one IP. You use portmapping to make it possible for several computers on your network to share a single outside IP.

All kinds of sub-types exist, but these are the basic types.

Here's a link on wikipedia with some more information: http://en.wikipedia.org/wiki/NAT