To get the caliber and type we need an accurate measurement of length and diameter in 100ths of an inch. It's fairly old based on the patina, but the reeded groove dates it to after 1880.
You usually if not always see that groove on jacketed bullets.There was no need to jacket bullets during the black powder era.Higher velocities with the use of smokeless powder made bullet jacketing a necessity otherwise the rifling in the barrel would just shave lead off of a bullet causing a deformed bullet.