Well to be fair. There is a little more to it then that.
Normally with IP Pass-through, which is also known as Bridged. You don't have to have a static IP for this so its not just to assign an IP. It also unlock the modems firewall and NAT features and passes down all traffic to your router directly. No block, no protection, no nothing.
NAT is "Network Address Translation" When data hits your public IP address, it needs to know where to go. This is what NAT does. Example would be this.
Your Desktop PC @ IP 192.168.1.5
Your Game Server @ IP 192.168.1.10
Lets say you are hosting a game server on the above IP 1.10. and lets say you also play the same game on your Desktop. Now when someone puts in your public IP to try to connect to the your Game Server. How does the router know what system to send that traffic too? How does it know to send it to your Game Server and not your Desktop PC? With NAT. Your router rule states open XXXX port and forward that traffic from your public IP to your internal IP address 192.168.1.10.
That is just an idea to help get your head around the question. They are two totally different things. IP Pass-through deals more with Public IP allowing unfiltered traffic to your network and removes NAT so your router can handle NAT.
And NAT is as I described above. It simple translation of traffic from the public ip to the internal IP of a system.
P.S.
I have a Plex server at home and all it required was to make a NAT rule in my firewall to allow the ports out and done. However, I also have Bridge/Pass-Through enabled with my ISP because I want to control all traffic from my PFSense firewall and not allow ISP to block anything passively.
So if you have a Plex server and allowed it through your router but its still not working. It could be blocked at the ISP modem. This is when you dont have IP Pass-Through or Bridge enabled. You get a Double NAT. Meaning your router and your modem are both doing NAT and one could be blocking it. Double NAT is bad. If you have your own router and know routing basics. I would always recommend you turn on bridge/pass-through on your modem to avoid Double NAT.