Yes. Gold figures are for 24 karat, silver for 999 fine. Jewellery is usually lower purity and worth proportionally less, and shops add labour and margin on top.
Precious metals trade internationally in troy ounces, which is 31.1034768 grams, while local markets quote grams. This page shows both, so you never have to convert by hand. The troy ounce is not the everyday ounce of 28.35 grams.
The central bank feed publishes gold with too few decimal places to be usable: a single digit change would move the price by hundreds. Gold is therefore refreshed from live exchange quotes for two tokens that each represent one troy ounce of vaulted gold, checked against each other before use.