Im not sure the dates these were used. I know they were used in the Victorian era and BuckleBoy finds them at mid 1800 sites so mid1800's to early 1900's is guess. The pic is from 1895 Montgomery Ward catalogue -(mojjax)
Yes picture rails clips, as a finish carpenter I install a lot of picture rail molding, though sometimes it is still used to actually hang pictures, but mostly it is to have the look of the homes built years ago, the link will show modern clips and what picture rail molding looks like.