The button is a relatively more modern fashion button, roughly copying the style of a U.S. Navy button. The wide border detail, crude die-work, black enamel type "false patina" coating, poorly constructed heavily rusted back, are but a few of the factors that undeniably account for this being a 20th Century fashion button, navy style, worn on blazer coats and sport coats.
Above the button, are more modern machine made bullets. To the right in our view, round pistol or rifle balls, dating from the mid 19th Century on back to earlier times. The flat one-piece button on the left with the "GILT" backmark, dates about 1820-1840, and could have seen use in the Civil War period, although this is generally a civilian type of button (assuming the face is entirely plain with no markings).
CC Hunter