If nmap reports a port is open, does that ALSO mean a service is listening on the port?

I have a Thompson TG585v7 router/firewall whose firewall is configured to FORWARD several ports to a computer X54 within the LAN.

These ports are in the range 1024 through to 2500

That X54 computer is now gone and so there is nothing "listening" on those final destination ports

If I use scan the firewalls public IP using

nmap -O -p 1000-2500 219.xxx.xxx.xxx

It reports other fully functioning ports that are open and have a service listening, but doesn't show these ports that are forwarded to a non-existant machine.

So My question is, if nmap reports that a port is "open", does it mean that both the following is true?

1. the firewall is accepting connections on the given port


2. there is a machine/service listening on the other end