Thank you very much for providing Digital Caliper measurements of your bullets.
The first one is a civil war yankee "Machine-Pressed-&-Turned" bullet... manufactured by a machine which compressed a lead slug into the desired bullet shape, then cut body-grooves into it by turning (spinning) it on a lathe. Note that it has an "ellipsoidal" base-cavity instead of a conical cavity. The type you found is incorrectly called a Belgian in some older bullet-books -- but proof has been found in yankee Ordnance Department records that it is yankee-made, not imported from Belgium. Yours is shown (as a Belgian) in the ancient McKee-&-Mason book, and as an MP&T bullet in the 2007 Revised Edition of the "Handbook Of Civil War Bullets & Cartridges: by James E. Thomas & Dean S. Thomas.
The second bullet, a fired one whose front got distorted by impact, is mysterious. It is definitely a metallic-cartridge bullet. The only match-up for a solid-based 3-groove bullet of the APPROXIMATE size of yours is a .32 Smith & Wesson bullet. But your photo shows yours as measuring .279 in diameter. Are you sure your caliper's jaw-blade isn't down in the bullet's body-grooves? I'm asking because there is no .28-caliber 3-groove bullet in the civil war era.
