You don't exactly get pure substances in the world. Soo, very much so, there are differences. Get a couple sorts of salt. Dead sea, Mediterranean, and the generic stuff, and you can certainly tell. Whether or not they have health benefits...
So the body is craving for salt, or craving for impurities?
Feed it the one it needs. If the body needs impurity x, which is tastily packaged with salt product y, advising to eat y seems like the sort of behaviour the OP is trying to avoid.
Yes. "Table salt" generally has things like anti-caking agents. A good quality sea salt has things like an assortment of 80-some-odd micronutrients found naturally in sea water. I have found it makes a big difference for me.
Is there often a difference between various sources of NaCl? ;)