There are some stateless things that are also called NAT, sure, but that's not what we're talking about here. (Fairly obviously, since a stateless mapping doesn't and can't save addresses).
I suspect when people talk about "NAT" in the context of a residential connection, what they actually mean is a "default-deny firewall with connection tracking".
(Are you going to point out that statelessly blocking a fixed IP range used to be called "firewalling" so a device without connection tracking can still technically be a "firewall" next?)