I've never been able to tell the difference, but...
Apparently, your generic Morton's table salt has anti-clumping stuff added and somebody, somewhere, can tell the difference. Kosher salt is also coarser grained and the size and shape is supposed to allow it to absorb more moisture than other forms of salt and this is supposed to make kosher salt better for curing meats.
My palette is pretty unrefined so I won't pretend to defend either position. I will say that, when the recipe calls for "Kosher Salt", I use Kosher salt. It's cheap and why mess around with a good thing?