If for example I connect to PIA VPN, and I hover over the icon on my toolbar, next to the volume, wifi, and battery symbol on a mac, it shows me one ip address (IP A) that is different from my actual IP (IP O). When I go on PIA's website, it shows me a separate IP address (IP B) however it says I am protected. The IP address on the website (IP B) is different from my actual IP address (IP O) as well as the one that is on my toolbar (IP A). What IP address is being used? Also, how many IP addresses do we have? And which IP address does the VPN hide? And if it doesn't hide the other IP address, how can I hide that?
Hard to sort this out without more info, but I believe:
IP A is probably a private IP only used inside your network (10.x.x.x/192.16.x.x/172.16-31.x.x)
IP O is your public IP (what the rest of the world sees, pre-VPN connection)
IP B is the IP the VPN gives you to browse the web
Go to something like https://www.whatismyip.com/, that'll show you what the world will see as you browse.