Here are two of those early soft-copper cases.
The one on the left is a .45 Schofield for the Smith & Wesson Schofield revolver. The one on the right is a .45-70.
Both appear to be rimfires, but they have the Benet inside-the-case center fire primer, which is identifiable by the crimp just up from the case head.
The Benet primer, developed at Frankford Arsenal in Philadelphia, allowed a centerfire round in a case that was made of copper, which was simply too soft to support a Boxer or Berdan style primer.
I figure both rounds were loaded sometime prior to 1885 or so, when drawn brass cases finally came into service.