"Some confuse NAT and firewalling because NAT effectively implements a default-deny-all-not-initiated-here rule in one direction which is what most home users want in a firewall."
To make it even more confusing what most people are confusing with firewalling is actually NAPT which is the specific type of NAT described in this thread. There are other types of NAT which don't require keeping track of state and which don't provide the default-deny-all-not-initiated-here rule side benefit.
> what most people are confusing with firewalling is actually NAPT
Yes. I should be clearer myself as just referring to NAT this way could serve to increase the confusion.
What most people just call NAT, what is offered by simple home/office routers (or APs when not in bridge mode or similar) and phones in tethered wireless mode, is actually NAPT (Network Address Port Translation), which is a subset of SNAT (Source Network Address Translation), which is in turn a subset of NAT.
To make it even more confusing what most people are confusing with firewalling is actually NAPT which is the specific type of NAT described in this thread. There are other types of NAT which don't require keeping track of state and which don't provide the default-deny-all-not-initiated-here rule side benefit.