Since 4 hours have passed without anybody else answering your ID-requests, I'll speak up. The button is a "Great Seal" US Army uniform button. Your has a raised rim encircling the emblem, and lacks any trace of the "black finish" used to camouflage the shiny brass front prior to 1923. So, yours dates from sometime between that year and the present. Most metal military buttons have a manufacturer's-marking on the back, called a "backmark,"which can help to narrow down a button's time-period. If yours has a backmark, please post a well-focused closeup photo showing the button's back.
I do not recognize the very-detailed emblem on the silver pin you found, but it has the 20th Century version of the British Royal Crown above the emblem. Please post a well-focused closeup photo of its back.