The only similarities between that crab and the millions that I see everyday in the marsh, whch we call fiddler crabs, are 1) it's a crab, and 2) the one large claw vs. one small claw, yet even in our fiddlers, only the male has the large claw. Female fiddlers have 2 small claws.
BTW, fiddlers make great bait for sheepshead fishing.