Welcome to Coin Talk. Other than a minor difference in grade I don't see any difference. Where do you see any difference? A little info on Peace dollars: https://www.pcgs.com/coinfacts/category/peace-dollar-1921-1935/26 If I were a little tech savvy, I'd do an overlay of both photos. But, I'm not. lol
On closer inspection they aren't too much different, just the wear is making me see them as different. Oh and show both sides of the coins.
Welcome to CT. The high relief is only for the 1921 (I think) and environmental factors and wear can cause color and luster differences.
From NGC's site... The 1921 Peace Dollar design was originally sculpted in high relief. Unfortunately, because of the relief, die life was much lower than acceptable levels. The coins had to be struck with such high pressure that the dies simply shattered under the strain. Because of these die issues, a new lower relief design was implemented in 1922. However, some proofs were struck in 1922 that were of the high relief type. They are exceptionally rare today. OP's coins are not the 1922 proof high relief rarities.