Fineness
Purity expressed in parts per thousand rather than karats. 999, 916, 750 and 585 are the numbers you will see stamped.
Fineness is the international way of stating purity, and it is what actually appears on a hallmark.
The conversion is straightforward: divide the karat by 24 and multiply by 1000. 22/24 gives 916, 18/24 gives 750.
Silver uses the same system, which is where 925 for sterling comes from.
When you are buying
Learn the four gold numbers and you can read any hallmark without asking: 999, 916, 750, 585. They are more reliable than a karat claim in a listing, because they are struck by an assay centre rather than typed by a seller.
Karat
The purity of gold, measured in twenty-fourths. 24K is pure gold; 22K is 22 parts gold to 2 parts other metal.
916 Gold
The hallmark number for 22 karat gold, meaning 91.6% pure. The same thing as 22K.
750 Gold
The hallmark number for 18 karat gold, meaning 75% pure.
Hallmark
An official stamp certifying precious metal purity. In India, BIS hallmarking is mandatory for gold jewellery.
925 Sterling Silver
An alloy of 92.5% silver with 7.5% other metals, usually copper. The international standard for silver jewellery.