bkay, I would say you have feet that fit more than one machine. One thing I've found is when the foot has that slot cut in the top part, that lines up with the needle hole, so you can see that those have a needle hole that is off-center. However the underbraider attachment looks like that which fits White, and White and National both have center needle holes, but the distance is just slightly less for the National, so if you put a foot for a National on a White, you'll break the needle as it won't go through the hole.
One if the reason I bought so many different machines was so I could check out the difference in how the attachments fit. And for most, they are unique is some way, so one way to help tell who made a machine was to see which attachments fit.