One might think that an ounce of gold or silver is an ounce of gold or silver. But several things enter into the picture to make the situation a lot murkier.
One is numismatics, the "coin collector" mentality that gushes over appearance, rarity, unusual features, historical significance, etc. Very much like regular coin and stamp collecting, but leaking over into the bullion market to distort things. Yet you can find a price on a given coin that has been numismatically "graded" highly and even packaged into a plastic "slab" with incorporated certification documents... that is cheaper than a raw commercial coin even from the same dealer. In theory though graded coins carry higher premiums.
Another is liquidity. In the US it is easier to sell or trade a US Minted coin (Eagle, Buffalo) than other forms of gold or silver. Next comes Canadian coins (Maple Leaf), and then UK (Britannia). Below that comes other coins from those 3 countries, then coins from Australia and South Africa, then "medallions" from the US Mint and others, and down and down in a loose hierarchy.
Another factor is premiums. Different forms of gold and silver have different markups, usually higher for the most liquid coinage. These can also fetch a bit more on buyback too of course. Premiums are not constant. There have been times when American Silver Eagle coins have had 100% premiums.