What is the IP address that I am connected to?
Always to your ISP's gateway.
In other words, to which IP address my ISP sees that I am connected?
Your VPN provider.
(and that's not really in other words, the two questions are distinct)
Is my public IP address the same of the IP address that I am connected to?
You should be able to answer that question yourself now.
It's not about where you connect to but about what the world sees...