No. That process was not used until test pieces in 1964 for the 1965-1967 coinage to be used in place of Proof coins on the 1965-1967 SMS coins. 1909-1916 had Matte proof coins on the cents and nickels that were a different finish. But nothing special on the 1938-S coins. 1936 had proof sets, but they look nothing like the SMS coin. It is the striking process that creates these. Not a die state coin issue. Nothing I've seen about this for that year. There are always EDS coins each year as the die are fresh on these strikes: They show fresh dies.
you've very observantly noticed the sharpness of the devices on your nickel, such coins are generated from fresh (unworn) dies, and are generally considered the most desirable examples for their grade
SMS coin sets didn't start (for the general public) until 1965. There were a few experimental sms sets in 1964 but not many - I hear like only 15-50 were minted.
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