Checkers, I had them when I was a kid. Or generic game pieces that could also be used for Backgammon or Parcheesi or ???. What I mean is they would come in a boxed set that had many different board games.

Carroms are rings, hollow in the center. Wood in the old days, I've seen plastic, not sure when that started.

Now the mix. Say someone made a Carrom board, with checker board on it and other games. I suppose the solid turned pieces could have been included. By the way, Carrom was played with your fingers, not some stick! So there are solid Carrom pieces, identical to the ones in your image. There are also checkers just like the game pieces that you show.

If I had to say, it would be, wooden game pieces without a definite origin. 50s and earlier.