The Baltic is a young sea that formed after the last Ice Age, about 10,000 years ago.
On the other hand, Baltic amber formed in the Eocene Age, over 40 million years earlier.
Today, the Baltic Sea is located on top of the amber deposits and washes the amber out of them, moves it with the sea currents and casts it onto the beaches. It was the Baltic that gave people their first pieces of amber, hence the name Baltic amber.
The mineralogical term for Baltic amber is succinite.
