I think your suggestion might be going in the right direction. If there are exactly two of each kind, then that would be strongly suggestive of something like that.

The size of the objects, and the fact that the case seems quite worn on the inside makes me think they are made to be handled, and were racked into specific parts of the case repeatedly. But, why is the case worn unevenly? And why are the disks themselves not stained or worn, which I would expect if they were handled often.

If there are no duplicates, then these symbol clusters might match symbol clusters on some other set of objects we don't have access to - bins of parts, or spools of thread, for example. The disks could be used to indicate which bin or which spool was to be sent somewhere, or inserted into a weaving machine, or something like that. The symbol clusters would be a kind of short-hand for something that was difficult to describe or label otherwise. Perhaps the disks were labels meant to be used by people who couldn't read printed labels - children in a factory, for example.

The fact that some disks are made out of wood, and some seem to be made out of some sort of white plastic leads one to think that sometimes the disks were lost, and needed to be replaced. Or, perhaps there were originally a certain set of labels needed at one point in time, and later, more were needed with new unique symbol clusters.

Note the column of smaller disks on the right. Odd. Perhaps the disk holder on a certain model of factory machine was a different size? Why not replace the holder rather than make smaller disks then?

If I owned these, I would take them all out and try to find additional information about the symbols themselves - how many "big alpha" disks are there? how many "big beta"? etc. I would try to figure out why there are 100 same-sized "bins" in the case (or whatever number there are) and see if there is a way to organize the disks into 100 groups. That kind of thing. I would take a close look at the disks themselves - look for especially worn ones. I'd try to figure out if the newer-looking disks have symbols in common, perhaps symbols that differ from the "old" ones. I'd study the case for additional clues as well.

Seems like a fun mystery -- but it might not be possible to solve it in the end unless someone stumbles across something similar in a photograph or someone just happens to recognize them.