Kind of blind leading the blind situation here with the person on the phone, guessing they dont understand much more then what the screen is telling them.
Public IP is the address from your ISP.
Private IP is the address your computer/device gets from the router
Static IP means your IP address (could be public or private) remains the same, hence static
Dynamic IP means your IP address (could be public or private) changes regullarly.
Port forwarding means you are allowing unsolicited traffic (meaning your router did not spicifically pre-request the traffic) through the router and to a specific PC/device and a specific port number.
This can be done with a static or dynamic Public IP.
If you have a Public IP that is dynamic, then you can use what is called a DynamicDNS provider.
You sign up for an account and get a URL from the DDNS provider (like yourusername.dyndns.org) . You then configure your router or run an app on your PC that will alert/update the DDNS provider when your Public IP changes, thus your URL will always redirect to your public IP
Thus you can still run servers at home and accept incoming web traffic even if you have a dynamic Public IP. You just need to setup both port forwarding and have a DynamicDNS service setup.
FYI most ISPs will block common ports on residential conenctions, so you wont be able to use ports 21-25, 53, 80 or 443 with most ISPs. You can set the incoming port to say 8880 and have it forward to port 80 on the PC and this will work; however you will need to manually set the port number in the browser (http://yourusername.ddnsprovider.com:8880/rest-of-url-if-needed)