Why is squid ink safe to eat, while skunk spray is not? What makes the two liquids different from each other?

They smell terrible and they’re very flammable, like methane gas. Many thiols are part of normal human physiology, but some of them are toxic.

The major thiol of skunk spray is (E)-2-butene-1-thiol, shown below. At high concentrations, it is toxic to humans, and has even been used as a biological weapon (if extracted from skunks) or chemical weapon (if laboratory synthesized).

Squid ink is meant only to conceal the animal so it can escape; it doesn’t need to be toxic to do that. Skunk thiols are meant to smell repugnant and irritate the eyes and mucous membranes, deterring enemies from approaching them.

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The skunk's anal gland secretions contain seven major volatile components: three major thiols, three major thioacetates, and a methylquinoline. These are divided into thiols and acetate derivatives of the thiols. Two of these thiols, (E)-2-butene-1-thiol and 3-methyl-1-butanethiol, are responsible for the repellent odor. These two thiols constitute 51% to 70% of the anal gland secretions.

Squid ink is composed mainly of melanin and mucus, but with smaller amounts of dopamine, L-DOPA, and a few amino acids—nothing toxic. These are also natural parts of the human tissues.

Skunk spray is a mixture of thiols (mercaptans), which are small organic molecules with a sulhydryl group (–SH). Here is one of the simplest, methyl mercaptan.

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That article goes on to describe the toxic effects of skunk thiols, mainly on dogs and cats.