In 1964, the United States faced a coinage shortage. Due to this, the mint ceased production of normal proof coins, which required significantly more work with die and planchet preparation. As a substitute, they created the Special Mint Set, which contained coins that weren't quite proofs, but were clearly of a higher quality than normal circulation coins. This allowed the mint to place more resources into producing coins for circulation. These special sets were issued in 1965, 1966 and 1967 before normal proof production started once more in 1968. I believe your coin is a normal SMS quarter.
Could you please post a photo of the edge? If you can't see the copper core it's probably plated. Here's a photo of a plated quarter's edge recently posted by another member.
What do I know...but, the lack of detail on George’s hair and on the eagle’s wings makes me think it is plated.
From your photos, it appears to be a circulated coin and I believe it was plated to make it that shiny, but it's hard to tell much without having the coin in hand.
To me it looks like it was buffed with a soft cotton buffing wheel. It wouldn't take to much to make a clad quarter shine like that. Similar to being whizzed but, with a cotton buffing wheel not a wire brush. This is very easy to do. It would only take a few minutes to do.
