Thank you for saving we ID-helpers the trouble of asking you to provide the PRECISELY measured weight of the objects.
Attaboy!
A fired musketball or bullet's shape can get unrecognizeably changed by high-speed impact... but its WEIGHT doesn't get changed, unless it hit so extremely hard that part of its body "splattered" off. For example, even though a lead ball is smushed enough that you cannot get an accurate measurement of its diameter, its precisely-measured weight can still help you ID it. We compare that weight with the well-documented weight of various calibers of musketballs and pistolballs, to see if there's a "very close" match.
Going by the weight measurements you provided:
The 307 grain weight of the larger damaged ball (I'm sure it is not a Minie-ball/bullet) works out to being a .59-inch diameter ball, which is the correct diameter to fit a .64-caliber English Musketoon. (That smoothbore musket is listed in the McKee-&-Mason book on civil war bullets & projectiles.)
The 79 grain weight of the smaller damaged ball works out to .38-inch diameter, which is correct for a civil war era .36-caliber revolver, such as the .36 Colt. I should mention, a 000 buckshot is .36"-diameter, but your 79-grains ball is heavier than that size.
