What's a coin?
A coin is bullion that is issued by a government mint and recognised as legal tender, and it's recognised worldwide. It has a face value, although this value is largely symbolic.
Examples include:
American Silver Eagles
Canadian Maple Leafs
British Britannias
Australian Kangaroos
What's a round?
A round is a minted bar in coin shape. It is usually privately minted, not legal tender and not recognised worldwide.
Examples include:
Ainslie Minted Silver Rounds
Scottsdale Mint silver rounds
Rounds are sometimes casually called “coins,” but they are not technically coins because they are not government-issued.
Does the difference matter?
Not to us. We buy back coins and rounds the same way, based on metal content and spot price, not legal-tender status. Where it can matter: coins are more widely recognised if you ever sell elsewhere, and in some jurisdictions legal-tender coins are treated differently for tax (check with your accountant).
Disclaimer: The above is not financial advice.