Why some months have more than one birthstone
Birthstone charts have changed over time. Some months gained alternate stones because jewellery trade groups updated the modern list, while older traditional lists kept earlier stones in circulation. June, August, October, November, and December are especially likely to show more than one accepted option.
That does not mean one chart is “wrong”. It usually means different publishers are drawing from different editions of the modern list or from older traditional references that still remain popular.