NAT & PAT are several ways to translate the private ip`s to real ip`s inorder to go through the public internet .
NAT (network address translation ) and it represent one-to-one technique (one real to each one private ) it has 2 types
1 - static NAt the admin. configure each private ip a certain real ip
2- dynamic NAT the admin. create a pool of real ip`s and each private ip wants to navigate through the internet take the first unbusy real ip in the pool table
PAT (port address translation ) it represent many-to-one technique all the private ip`s navigate through only one real ip put the difference here from NAT that PAt include the port number with each private ip go through the real ip ,so all the private ip`s take the same real ip but with different port number.
i hope you understand