The Private IP address represents the address assigned by your organization to your local workstation. For instance, in the screenshot above, address 10.XXX.40.37 is the address of my workstation once in my company's network and connecting to PAM. From any client connecting to the appliance, ipconfig /all will confirm this is the IP assigned to it and visible within your organization
The Public IP is thepublic-facing IP that your ISP has provided to your workstation. For instance here 185.41.96.XXX is the IP that the ISP has assigned to my workstation for connecting to remote servers: any of them will see my connection as coming from this address.
To confirm this you can use any third party utility, like for instance https://whatismyipaddress.com/