All salts are pretty much sea salt, because they pretty much all come from the sea. (Unless they come form inside a volcano....see below.)
Table salt is processed to remove all the elements and trace minerals, which are actually good for you. They add iodine back in, but nothing else.
Pink Himalayan salt and Indian black salt are both unrefined and have different and stronger tastes than processed salt.
The ultimate salt experience can be had at the beginning of one of the most expensive meals in New York: at Thomas Keller's Per Se in Columbus Circle.
With the bread and butter, the waiter puts down a "selection of Artisinal Salts," which includes six salts: one from the Dead Sea, one from Iceland, one from Bolivia and the one that came from inside a volcano in Hawaii.
Here's an interesting (if typically pretentious) article by Mimi Sheraton on searching for salts.
SMITHSONIAN: Mimi Sheraton's Tasting Tour of Salts Around the World