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.
The shield/ coat of arms is Canadian Dominion of some variety, with the closest match I found on the 8th item at the link below. This happens to be on a military item, but that doesn't mean that everything with this shield is too. The particular pattern seems to just barely pre-date the 1901 date on your item... Perhaps the manufacturer wasn't yet aware that the pattern had been changed? JK Militaria offering Canadian militaria, badges, medals and insignia from WW1, WW2 and earlier.
Thank you for providing a closeup photo of your button's back. The only lettering visible is "No. Attleb" -- which is enough to prove the manufacturer is D. Evans & Co. of North Attleboro Massachusetts. That company stopped making buttons in 1945. So your "Great Seal" US Army button was made sometime between 1923 and 1945.
Furthermore... because the US Army's size shrank drastically after World War One, comparatively few buttons for it needed to be manufactured in the 1920s and 1930s. When the army's size expanded enormously to cope with World War Two, multi-millions of new uniform buttons had to be made. So, the "statistical odds" greatly favor your button being manufactured during World War Two rather than during 1923-to-December-1941.