My grandfather had a handful of similar medals from events like conventions. As a kid I thought they were coins.
A web search just now, using the terms "souvenir: medals, badges, tokens or whatever I could think of" has lead me to believe that people will sell mementos of any event where they think they can make a profit. I wouldn't be surprised if they sold them at public hangings.
A large quantity of the small ones would go through lapel button hole, so lapel pins would be my best guess.
The Clemson badges look like collectible coins of some sort, but there’s nothing on the back! No threaded stud or any kind of engraving.
The bigger ones seem like theyd be mounted to a door with a decorative screw? However, the hole is really big, like 5/16”.