The lower picture you show is either a model 1840 or an 1842 not an 1816, the cutout in the top is squared off at the bottom on an 1816, but is yours made of brass or steel? Oh great find by the way, you gotta love finding gun parts!
I'm sorry it's a model 1842 smooth bore musket. It was made at the Columbia SC armory by B Flagg and William Glaze (out of SC). Only 6,020 of these muskets were produced in the Columbia Armory and were distributed to SC militia. B. Flagg made his muskets from brass rather than iron.
Thanks buckleboy! I found it at a SC camp and I believe it to be from the Columbia Armory and made by B. Flagg and William Glaze. The Columbia Armory would distribute these weapons to the SC infantry. The only two people that made these weapons with brass on them were B. Flagg and another man who's company went under before the war.