The first bullet is a fired .45-70 caliber US Model-1873 Springfield "Government" Rifle bullet. It was in US Army service from 1873 up until World War One (for training new troops). That is why many-many fired .45-70 bullets are found around the Chickamauga Battlefield Park (in NW Georgia) where army troops trained for the Spanish American War in 1898.
The second bullet is a .50-70 caliber "Model-1866 Government Rifle" bullet. Like the US .45-70, the .50-70 stayed in service for troop-training use long after newer improved models of US Army rifles were introduced. Also like the .45-70, after newer models were adopted, many .50-70 rifles were sold to the public as Military Surplus, for big-game hunting. So, we relic-hunters dig bullets for those rifles far from any army-activity sites.
Thanks for the history lesson. I had no clue as to what they are.