How is NAT different from regular "routing"?

Question

Network routing

What's the difference between NAT and a regular server that distributes IP addresses for its internal network?

Answer 1

Like between NAT and DHCP.
NAT translates addresses, DHCP distributes them (not only them).

Answer 2

These are two completely different technologies. They go hand in hand, but it's no problem to use them separately.
DHCP without NAT - any home network with "white" addresses, which automatically distributes them.
NAT without DHCP - no problem to do it on a regular home router.
How NAT works. We take and correct some parameters in the outgoing packet, such as the outgoing port (to find out whose packet). At the same time, we change the outgoing address to the external network address. When the answer comes, we restore the original subscriber, change the incoming address to the address of this subscriber and relay it to the internal network.
The task of simple routing (which is not NAT) is simply to transfer the packet further along the chain, reducing the TTL and determining from the routing table which connection it should be transmitted to.