Your public IP address is what remote servers see, assigned by your ISP or mobile carrier and often shared across many devices behind the same router through NAT, or rotated periodically. This page calls the ipify.org API to report your current IPv4 and, if your connection supports it, IPv6 address, alongside details your own browser exposes such as language and connection type.
Your IP can change between requests if your ISP rotates addresses, or if you're on a VPN or proxy for one connection and not the other, this page shows the address seen at the moment the page loaded.
Not every ISP or network has IPv6 enabled yet; if your connection is IPv4-only, or your router blocks IPv6, only the IPv4 result will populate.
No, the lookup happens client-side against a public API and nothing is retained by this site; reloading the page simply repeats the same public lookup.