Open Nat (type one) -dmz, port forwarding or upnp
Moderate nat(type 2)- port conflict, port translation issues, upnp not forwarding requested port, external port does not match internal port.
Closed- haven't seen this one before but it exists.
Strict(type 3) -port is blocked and upnp is disabled or not working.
Symmetric If I remember correctly is open on one client and moderate on the second.
Restricted and
port restricted I'm sure is both strict nat, you missed
address restricted.
Put it this way xbox needs open nat to work properly, even Microsoft says so that's why it's extremely important, at least now Microsoft is releasing an update to allow users to change the consoles port number, I wish Sony will follow in suit.
Heres something I found in Reddit
Open: XBL port or alternative port is open inbound and outbound.
Moderate: XBL port is open outbound, but not inbound.
Strict: XBL port is unusable and an alternative port is used. This alternative port is not open inbound
https://www.reddit.com/r/xboxone/co...rtsymmetric_nat_what/?st=j67ebjq5&sh=3babdef8