what is the difference between "DHCP and NAT" and "DHCP" router modes

DHCP alone is used where you buy a block of public IP addresses.. each time a computer connects it will request another IP.. which is sourced from the ISP not the router.. This is extremely rare setup.. (for home users that is.. multiple public IP blocks are expensive). It could be used with another router as a true router rather than NAT.. Even with a private IP address setup you will seldom do it this way.

For everybody the option we use is either DHCP and NAT.. where the router takes a single public IP and uses a translation to (Network Address Translation) to a range of private IP addresses.

Or bridge mode.. where the TC is plugged into another NAT router.

Some of what LaPastenague said is correct. Most home routers use DHCP to assign private IP addresses to your private local network.

NAT means that data from the private IP addresses is translated to go across the public internet IP.

LAN (private IP addresses assigned by your router using DHCP) ------------>router (uses NAT to translate the network addresses)------>internet (public IP address assigned by your ISP)

EDIT: and to answer your question, you will always use NAT as long as you have a home network. You will also always use DHCP, unless you are assigning static IP addresses for all of your network devices.

yes, you have it right. Except your timecapsule doesn't use DHCP to get the IP address from comcast. Possibly, Comcast leases it to your modem with their own DHCP... this public IP gets passed to your timecapsule. But the rest of what you said is right.

The only reason you would turn off DHCP or NAT would be if you have another router or server on your network that is already running DHCP or NAT. Some device on your network needs to run them though. Most likely, it is going to be your timecapsule.

NAT I suppose is used to allow me to use my internal addresses for me at the same time other people are using the same addresses on their private networks and there is no clash?

NAT saved the world from having to go to ipv6 ages ago.. otherwise we would need every device in a network to have a public IP and the routing issues would be considerable.. protection of private networks a nightmare.. if you think the current virus/trojan/malware situation is bad (less so on macs of course).. if everybody had every device they own fully exposed it would be a nightmare.

But NAT introduced a whole new set of problems where access to the internet for direct communication is subject to painful issues.. so anything that is interactive, games, voip, messaging etc requires opening of ports.. which would not be needed in ideal world.

Now that ipv4 is practically exhausted, we are going to be forced to ipv6.. but it is not an easy transition.

So for home use I need "DHCP and NAT"

Yes, until ipv6 starts up and we start down that track.. for now.. NAT is required.