Understanding the difference between DHCP and NAT

I was recently reading up on NAT and as I know it acts like a DHCP server, I fail to see the point of it over DHCP as it seems I can do the same thing.
With DHCP I would have a server with 2 network cards one external and one internal, the internal would be a private network and distribute IP addresses to clients whose IP settings were to obtain automatically.
These clients could then access the internet right as long as their default gateway was set to the DHCP server.

How is this different to what NAT does?

The client settings are the same (obtain IP automatically)
and it just maps ports to private IP address right?

If anyone can direct me to a detailed (but understandable) explanation I would appreciate it?

Also why you would use one over the other?
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stevenlewisConnect With a Mentor Commented:
NAT is network address translation. It does not supply ip adddresses to clients. They are often used in conjunction with each other (ICS)
NAT maps ip addresses to ports, so in effect the ip's of the LAN are "hidden", and all requests appear to come from the same ip
example private range of ip's can't be routed to the internet, so with NAT, the requests go thru the NAT and appear to come from a valid public ip. replies are then sent back to the NAT, and then sent to the original requesting machine.
DHCP (dynamic host configuration protocol) can provide ip info to clients who request it
the confusion comes in because ICS (internet connection sharing) does both dhcp and NAT
You can use NAT with static ip addresses, and you can use dhcp without using NAT (if you don't have a connection to the net) Your ISP (if dialup, and some cable/dsl) uses dhcp to provide ip info to the clients, but hands out valid public ip addresses (and so doesn't use NAT)
in fact on w2wk you have a choice of using ICS or NAT), and if you use NAT, you can set up a seperate DHCP server
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