Simple Concept behind port forward in NAT network

I think most of the household internet uses the NAT network. That is within the household, every device is having a unique private IPv4. Then many households are sharing one public IPv4. Suppose I set up a web server on local port 80 and then set the port forward from the public IPv4 port 80 to my local device. That means my web server is occupying the public IPv4’s port 80 and other households cannot port-forward the public IPv4 port 80 to their local device? Is my understanding correct?

Thanks!