I have a question about DHCP and NAT.
I know NAT translates local IP addresses and ports into a single IP address and specific ports that can be used to communicate with the Internet.
I also know DHCP is used to assign or re-use an unused IP address to a computer that connected to the network.
How does NAT obtain its single IP address? Does it use DHCP?
NAT and DHCP are totally independent technologies, which do not rely on each other at all.
The first concept to understand is one of network segments - simplifying slightly, all IP addresses in the same IP range are in the same segment. A DHCP server listens on a given segment for requests for an IP address and offers it when asked. A DHCP server needs to listen on the same interface as the segment is on - thus it can run on a computer with a single network card, or on a router (in a home network it would typically run on the router, serving addresses on the LAN network).
On a typical home router NAT is run on the WAN interface, and relables packets leaving the network with the external IP address. It holds a translation table so it knows which internal machine requested what. In this way its possible for a single real-world IP address to be shared between multiple workstations.
Your question "when I connect two different computers they both get different external IP's. How can this happen? Shouldn't my router be NAT since it protects my local IP Address?" presents something of a curveball. The answer is yes, in a home network, any devices behind NAT would typically share a single external IP address.
There are a few possibilities why you are getting different IP addresses, including -
Your provider is using Carrier Grade NAT, and and is, in effect doing double-nat. Carrier Grade NAT requires the use of more then 1 IP address, so it could be that different TCP sessions are being allocated different IP's
You may not be using NAT at all, and your provider is providing you with a subnet of IP addresses which are real-world routable. This would seem somewhat unlikely in a home environment (and indeed there are security implications to it), but not uncommon if requested on business accounts.
Its conceivable your router has more then 1 real-world IP address on it and is doing more complex NATTING (similar to carrier grade nat) to overcome some limitations of NAT.
