You can take a ferry from St. Thomas to St Johns (or back
), so they are not the same island
Every island has at least two sides
St. Maarten just happens to have two countries, on separate sides of the same island
And the island is small enough that you should be able to see some of both the French and Dutch side. Not a difficult island to find your way around, so no need to worry about getting "too lost" if you drive there.
If you didn't stop, it's only about a 1 hour drive to get all the way around the island.