There is only a sign between the 2 islands. It is accurate that the French side is more laid back and less touristy. The Dutch side is more party oriented and is where the Cruise ships dock and the airport is.
A couple other things to do:
If you go into Petersberg try to find a Non Cruise ship day. The shops are DESPERATE for customers and everything is heavily discounted, especially if you don't mind haggling a bit.
If you go to Marigot, check out the Bar de la Mer. Fantastic food and a great location at a reasonable price. As a trivia answer they set up a dock that isn't there and had the Cruise ship crash into Marigot for "Speed 2".
If you go to Orient, there is a lesser known but very cool little bar/restaurant on the opposite side away from the Nude side. They have the lobsters in the water right out front in their cages and will fix them for you.
If you have some time, you may want to see if there is a boat or other trip to St Barts for the day. That is a gorgeous island that feels like you are in the South of France, it's about 30 miles away. Very ritzy but amazing. We sailed across and they also have a tiny airport. You can also take a trip over to Anguilla but personally I liked St Martin better.