Terminology: Router, gateway?

I'm trying to understand the difference between these two. An 
off-the-cuff poll seems to result in this semi-consensus:

A hardware box called a router is a one Ethernet-in port, and one (or 
more) Ethernet-out port(s) product. Firewall, DHCP, and NAT are 
typical features.

A box called a gateway is all the above plus an integrated cable or DSL modem.

Any agreements or disagreements welcome.

Thanks,
Dave
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