The longer piece has a little scrap of red paper stuck on at the end; apparently a portion of a label of some kind with an ornamental border.

The other end of the stick has been broken off.

The shorter, stouter stick has had its central cavity artificially enlarged so that it fits over the other to form a cap or sheath.

Make a careful note of those facts and try to think what they probably mean; what would be the most likely use for an object of this kind.

When you have ascertained that, you will have learned something new about this case.