the one on the left looks like a little badge. I remember when I was young they came with pictures on them with a straight tab. You bent the tab down to fasten it on your collar, or where ever you wanted to wear it. Don't remember what they were called.
The random deal has a set screw in it you might try removing it and maybe by taking it apart it might reveal what it is it reminds me of a light socket for a lamp.(crushed)
minelab safari,whites m6, AT Pro, Ace 250 and whites coin master, Garrett AT propointer (garrett carrot), Lesche hand digger, 5x8 & 8.5x11 DD coils for the Pro, Camera is Ion Air Pro 3
That sort of clip thingy is (was) most commonly used as a museum admission button/tab... Not that I can figure which museum that would be if it happens to be the case. http://www.krausbanners.com/admission-buttons-tabs/