Intersting that you have them with the wing nut on different sides. Can you tighten them up that way?
That "foot" is the adapter - if you take the binder attachment off that other foot - then you have a different style adapter.
I have the first style for my Royal machine, but not New Home, I've seen the second style for New Home and Standard, but no other machine (so far).
Here are some of the other "adapters" I have.
