I still don't understand one thing, if HPS is used for pool payouts (as is displayed in the block distribution page), what purpose does HPS2 have and why is the leaderboard sorted by HPS2 by default?

I know HPS2 has something to do with shares submitted and luck, but is it used in the pool calculation for payouts or not? If it is used, then why is it not displayed in the block distribution page and HPS is displayed instead?