Which salt, and what the wrong one does
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What is actually different
Canning and pickling salt is sodium chloride with nothing added. Table salt usually carries an anti-caking agent to keep it pouring and often iodine for public health reasons, and both of those additives are fine in a salt cellar and visible in a jar. The published guidance names them specifically rather than recommending a brand.
What each additive does
The anti-caking agent does not dissolve cleanly and settles as a haze or a white sediment, which is indistinguishable at a glance from the sediment a ferment produces naturally and from the sediment that means something is wrong. Iodine darkens the product. Neither is dangerous and both make a jar look like a mistake.
Why salt is not seasoning here
In a ferment the salt concentration is what selects which organisms can grow, which makes it structural in the same way sugar is structural in jam. The published guidance gives salt by weight per gallon of container capacity rather than to taste, and a ferment brined by taste is a ferment running at an unknown concentration.
Substituting it
Kosher salt is usually additive free and is the common substitution, but crystal size differs between brands so a volume measure is not transferable. Weigh it. Reduced-sodium salts are a different matter entirely and should not be substituted into a ferment, because the thing being reduced is the thing doing the work.
Buy pickling salt in quantity before the season rather than in boxes during it. It is cheap, it keeps indefinitely, and running out mid-ferment is the kind of interruption that produces a substitution nobody wrote down.