My guess is that there are actually two interchangeable grapples. One open, with cord, and one closed, without.
There are, but Wor-Gar's comment is regarding the rope/string. Closed grappling hook has the string resting inside the box on the belt like in the movie, but the open one theoretically can be pulled out to look like you're going to throw it, but how do you get the string back into the box after pulling it out is the question.
Maybe each grappling hook has a different white box connected to also, so the rope doesn't go in, it just looks like it's in or out depending on which you use.