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Your larger bullet is a civil war yankee .58-caliber Williams Type 3 "Bore-Cleaner" bullet -- missing its hardened-lead "base thumbtack," which held a thin slightly cupped zinc washer. (See the photo below.) The washer's purpose was to help the bullet catch onto the gunbarrel's rifling-grooves, and also had the desirable effect of scraping some fouling (powder-ash and lube grease) out of the rifling-grooves, hence the nickname "bore-cleaner." But note, bore-cleaning is not mentioned in Mr. Williams' US Patent for his bullet... the bore-cleaning was just an unintentional side effect.
Your smaller bullet is from a brass cartridge-casing. It appears to be a .32-caliber revolver bullet. Unfortunately, it is definitely not a civil war .32 Smith & Wesson. Also unfortunately, there's no way to know with 100% certainty whether it was made during the civil war or a decade or two later. But it most likely is no younger than the 1880s, because its very-white patina means it is made of pure lead, not the hardened-lead alloy which superceded most pure-lead bullets by the end of the 1880s.