To make a long story short, no, not really.
The main difference is that regular ole’ refined table salt is much more likely to contain additives like anti-caking agents. North America has also been adding iodine to its table salt since the 1920s in order to avoid the development of goiter in the population, a condition that enlarges the thyroid and can lead to hypothyroidism. Most ‘impurities’ and trace minerals are removed, and the grains are extremely finely ground. The big differentiator is the addition of iodine, which most other salts will not contain.
Kosher salt is pretty much the same sodium chloride compound as table salt, but with a coarser grain. Jewish law mandates that blood be extracted from meat before it is eaten. Because of its flaky structure, kosher salt is very efficient at drawing out that blood, and is therefore quite useful for those wanting to keep kosher in their eating habits. Iodine and anti-caking agents are almost always left out of kosher salt.
Sea salt is distilled from ocean water and undergoes very minimal processing, which means it holds onto a lot of natural minerals like calcium, magnesium, zinc, and potassium. These minerals might be enough to affect color or flavor (as with Celtic sea salt and its grey-ish tones), but will not have a significant nutritional impact. The darker the sea salt, the more ‘impurities’ and trace minerals it will contain. It also usually appears in coarser, less-finely-ground forms than table salt. Fleur de sel is a type of sea salt that is harvested from the surface of salt evaporation ponds when it’s still “young”, or the crystals are freshly-formed.
Himalayan salt is mined from the Punjab region in the mountains of Pakistan, near the foothills of the Himalayas. The salt was shoved up into the mountains after being deposited from an evaporated ocean a few million years ago. It contains trace amounts of minerals like magnesium, potassium, and calcium which give the salt its signature pinkish hue.
Sadly, replacing your drab table salt with trendy pink crystals won’t have any real effect if your salt intake is still through the roof. But as far as those foodstagrams go, we support your use of any and all flakes available.