Yes, but it depends on which day of the month you were born.
Birthstones are gems assigned to the months of the year. Star
stones are gems or crystals that are associated with zodiac signs.
It is more likely that your birthstone and star stone are the same
if you are born within the last ten days of the month.
For example, the birthstone for July is the ruby, which is also
a star stone of Leo. If you are a Leo born in July, your birthstone
and star stone are the same.
However, if you are a Leo born in August, your star stone is the
ruby but your birthstone is the peridot.