<< To me a firewall is something that secures one network from access by another and NAT does this. >>
Well, NAT can't do this alone, it needs to run on some device. That device could be (and normally is) a firewall and NAT is one of the tools the firewall can use to do it's job (just as it can filter packets, establish VPN connections, etc.)
But what people choose to call a firewall depends probably on what they are used to. I would not call my ADSL router a firewall, but merely a router with very limited packet filtering capabilities, but the SonicWALL we use at work is a real firewall IMHO