Caroline,
Here is a comparison pic of the unidentified bobbin and the White / Kenmore type like you have:
You can see just how much smaller the unidentified one is. I actually tried it in the Kenmore's bobbin case and it almost jammed in it. The ID of the axle is just enough smaller than the Kenmore bobbins that it is too tight.
pippi65,
Why not post them? Weird things are interesting.
Joe