Sorry for posting before reading all the posts or even all the first post but NAT is not letting a bunch of computers use only one IP.
NAT is more like a condo time share for IP's. An individual or corporation would own a number of ip's (My local jc who I have done volunteer work for owns 4 blocks of 254 for a total of 1020.) but still more computers (the before mentioned jc has over 2500). NAT takes the available Public IP's (the ones owned) and tranlates them into internal Private IP's....
HENCE the prase network address translation.
There is a translation or mapping of the external to the internal ip's so that there is internet connection hopefully for everyone who is currently trying to use it. (First hand experiance is that on peek hours you will sometimes not get to the internet if you are on NAT.)
What you decribed is sometimes called address jinking or more commonly address Mascarade. It is often called NAT in low end routers. But, anyone who has worked on a network will be as quick as I have to explain the difference because we hate the marketing dept's that screw the public by telling them they are getting something they are not.
NAT for all its drawbacks (mostly the not always being able to reach the internet) works better then Mascarading. Let me explain. If I had 10 computers hooked through a cheap router that mascaraded and 3 people wanted to play EQLive; 2 of them would be disapointed. The neccessary PORTs to play would be in use by the first person. With only one address the ports not the address determine what can be done and each service is normally only set up to use ports in a given range. That is how a Http server and an Ftp server can both be ran off the same machine. On the other hand with NAT if I owned the right to use 4 ip's from my provider all three could be playing.
Only when a both a 4th and then 5th person needed access to the internet would anyone hear a complaint.
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