The short answer is yes. But it's not the only one that's "different." Sea salt composition changes from region to region based on a number of factors.
Basically, mineral concentrations vary from one ocean or body of salt water to another, making sea salt from different regions of different bodies of water chemically different. In theory, a chemical analysis could differetiate the filtrate of the Caribbean Sea from the Gulf of Mexico, though the two are linked. The minerals themselves might not be very different, but their concentrations could be very different.
Whether these differences make any one salt better than another for a given use is probably largely a matter of opinion.