From my weird lay understanding, it's somewhat similar to childhood games where people would try to determine who had the "coolest" Pogs [1]. There are multiple "axes" that determines which challenge coin "wins": highest rank associated, most interesting challenge involved (some coins represent specific deployments or activities or actions), perceived rarity (there only three of the coins ever made), etc. To some extent the challenge coins serve what medals/badges always have: an excuse to tell a cool story, maybe brag about something. Similarly the "free alcohol" rules follow the same general principles of "that's a really cool story, I owe you a beer for it", just reduced to simple evocative coin form.

Which "axes" are in play, and who "wins" (or ties, a lot of the rule variations I've heard are set up to optimize towards ties; the most common challenge is just whether or not the other person has a challenge coin of any sort, not necessarily trying to figure out which wins if both people have coins on them) varies a lot between groups.

Also, challenge coins have seeped into some parts of lay culture, especially bar culture (given that alcohol has always been the big bet, it shouldn't be a surprise). For instance, the liqueur Fernet has its own challenge coins that bartenders tend to challenge each other for free shots of Fernet. (Bars try to keep one in reach of the bar at all times in case the bar is challenged, and the number of people that have them that have them that aren't themselves bartenders is supposedly kept quite rare.) https://talesofthecocktail.com/history/part-family-behind-sc...

https://en.wikipedia.org/wiki/Challenge_coin

[1] https://en.wikipedia.org/wiki/Milk_caps_(game)