[fulafel]

What a consumer NAT box typically does is not routing. Routing is IP forwarding without messing with the packets. See the link in my post.

Here are various other kinds of middlebox devices that are also generally about connecting networks at layer 3 with various side effects vs routing (just like NAT):

http://en.wikipedia.org/wiki/Middlebox#Types_of_Middleboxes

None of these devices are internet routers. It's just wrong terminology.

[Dylan16807]

It does NAT and then it routes. In addition, any device with ipv6 support does the pure routing without messing with the packets that you speak of. It's a firewall and a NAT device and a router all in one. Sometimes it's a modem too.