The "regular" bullion American Silver Eagles you see being sold individually, in twenty-coin tubes, and 500-coin monster boxes are known as Brilliant Uncirculated, or "BU". This means that the coin was made using the normal minting process, and retains all its original luster. Usually only coins direct from the mint are designated BU. Also known as a "business strike" Silver Eagle, these unlimited-mintage coins are produced by the millions every month to satisfy demand.
Made from 1 troy ounce of .999 fine silver like all American Silver Eagles, the BU Silver Eagles are produced at the U.S. Mints at West Point, NY and San Francisco, CA. In past years, Silver Eagle bullion coins were also struck at the Philadelphia Mint. But since the Brilliant Uncirculated Silver Eagles do not carry a mint mark, it is impossible to tell where a particular coin was minted (unless you know that only one Mint made Eagles the year your coin was struck).
The Mint does not sell these investment-grade silver coins directly to the public. They are only sold to major bullion dealers such as Gainesville Coins, who then offer them to the public.