I typically use Kosher (Diamond Crystal) for cooking and seat salt on occasion for finishing, but at the end of the day, to me, salt is salt. And, one could probably argue that all salt emanates from sea salt.
To me, all salts are born equal. The basic composition of all salt is sodium (Na) and chlorine (Cl), and the ratio of the two in salt is approximately 40% and 60%, respectively. Most salts also contain a few trace minerals in miniscule amounts such as magnesium, potassium, sulfate, etc. The processing of the salt is what brings about the difference, and the difference is typically reflected in a ratio of volume versus weight. This presents a problem since almost all recipes call for "X" volume of salt rather then "Y" weight, and they all weigh differently at the same volume. Also, a few recipes may specify "Kosher" salt, but I don't ever recall one specifying a particular brand.
As Martin said above, Morton's Kosher salt, at the same volume, is 37% heavier than Diamond Crystal Kosher salt, and that's because Morton's Kosher is much more dense than Diamond Crystal Kosher. Taking it a little further, Morton's table salt, the densest of all, is 22% heavier than Morton's Kosher, and 69% heavier than Diamond Crystal Kosher.
I learned a lot of this the hard way a number of years ago after tossing a very delicate sauce that I had made many, many times because it was way too salty when I had to substitute Morton's Kosher for Diamond Crystal Kosher, using the same volume measurement as I always had. After doing some research of my own, and reviewing the research of others, as well as weighing different salts in the pantry, I was stunned at the different weights of the various salts at the same volume. Using Diamond Crystal Kosher as the baseline salt, the table below illustrates the differences.
Another thing I learned is that most professional chefs, and the writers of well regarded recipes, typically use Diamond Crystal Kosher, even if they don't specify it, as that is the salt most commonly used in culinary training programs. If you're following the recipe, and using a different salt, just back off accordingly. For example, if a recipe calls for 1 tablespoon of "Kosher Salt", and if I only had Morton's Kosher available, I would use 2/3s of a tablespoon. You can always add more if you want too, but you can never remove the salt if you've put too much in.