They look to be pre WWII to mid WWII style collar brass for the US Army, the one on the right is U.S. for United States, the one on the left is an Engineer disc. Both were worn on the collars of the uniform.
Honestly they look to have traits of several of the early variations. Look at the following link, with them in hand you might get a better match than we can. Photos are little blurry.
Yours look to be WW2 era pins to me. When you unscrew the nut on the back does the insignia separate from the disc or are they one piece? Also can you see any makers marks on the backs?