What is a mint?
A mint manufactures coinage. Sovereign mints are government institutions, the U.S. Mint, the Royal Canadian Mint, the Perth Mint, and their bullion coins carry a state certification of weight and purity, plus a symbolic face value as legal tender.
Private mints are companies. They produce rounds and bars, often to excellent standards, but the backing behind the product is the company's name rather than a state's.
Why does sovereign backing matter?
Trust travels with it. Any dealer anywhere will price an American Eagle over the phone because the U.S. Mint stands behind its content. That universal acceptance is a real component of what a sovereign coin's premium buys.
Private-mint products trade on the maker's reputation: established names resell readily, obscure ones get tested and discounted. The product may be equally pure, the market's confidence isn't.
How do mints show up in practice?
Watch for marketing that borrows government language, 'U.S. Mint design,' 'official tribute', on privately made products. If the product isn't issued by the sovereign mint itself, it isn't a government coin, whatever the brochure implies.