Yes there were restrikes and originals, and there are controversies over which are which. Generally a “coin turn” rotation (turn the coin head over heals) will result in the eagle with the right orientation flying “onward and upward is considered to be an original striking. Coins that are medal turn rotation (turn the along the vertical axis) with the eagle flying horizontally are generally considered to be restrikes.
David Bowers in his silver dollar books disputed that interpretation.
Retired dealer and avid collector of U.S. type coins, 19th century presidential campaign medalets and selected medals. In recent years I have been working on a set of British coins - at least one coin from each king or queen who issued pieces that are collectible. I am also collecting at least one coin for each Roman emperor from Julius Caesar to ... ?
Original: 1000 struck in Dec 1836, die alignment I (head of Liberty opposite DO of DOLLAR, eagle flying upward when coin is turned on horizontal axis from obverse to reverse, i.e., coin turn)
Restrike: 600 struck in Mar 1837, mostly die alignment IV (head of Liberty opposite F of OF, eagle flying horizontally when coin is turned on vertical axis from obverse to reverse, i.e., medal turn)
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Specializing in 1854 and 1855 large FE patterns
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David Bowers in his silver dollar books disputed that interpretation.
upward when coin is turned on horizontal axis from obverse to reverse, i.e., coin turn)
Restrike: 600 struck in Mar 1837, mostly die alignment IV (head of Liberty opposite F of OF, eagle flying
horizontally when coin is turned on vertical axis from obverse to reverse, i.e., medal turn)
I think this is correct.