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Arabic has سلام (salaam) and Hebrew has שָׁלוֹם (shalom). The words have similar meanings of "peace". This seems like a case of an alveolar fricative shifting to post-alveolar fricative (or vice versa)
Similarly, Hebrew has "ani kotev" while Arabic has "ana aktub"; like a bi-labial fricative has gone to a labial-dental fricative (or vice versa).
This seems to indicate the possibility of some rules about how sounds have shifted. Is there some equivalent of a Grimm's law for semitic languages?
Quite a lot of them, in fact!
Grimm's Law is probably the most famous description of a regular sound change. But there are an enormous number of these in historical linguistics, some named, some not.
For example, the correspondence between Hebrew /v/ and Arabic /b/ stems from a change in Hebrew and Aramaic called begadkefat spirantization, where the short non-emphatic stops /b g d k p t/ (hence "begadkefat"; F instead of P because it got affected by this change) became fricatives after a vowel. Some parts of this change then got reversed by later mergers, depending on dialect, but I believe all modern Hebrew dialects still have fricative variants of /b k p/.
The correspondence between Hebrew /ʃ/ and Arabic /s/ doesn't have any nice name that I'm aware of. Proto-Semitic is reconstructed as having multiple different "S-like" sounds: *s₁ ("shin") became /ʃ/ in Hebrew and /s/ in Arabic, *s₂ ("sin") became /s/ in Hebrew and /ʃ/ in Arabic, and *s₃ ("samekh") became /s/ in both Hebrew and Arabic. Based on these correspondences (and other data like Ge'ez *s₂ > /ɬ/), many scholars think that *s₁ was a sibilant fricative of some sort, *s₂ was a lateral fricative, and *s₃ was a sibilant affricate.
The axiom that all phonological changes can be formulated as exceptionless laws like this was a core tenet of the Neogrammarian school of linguistics back in the 19th century. It's not generally accepted nowadays (because there are, it turns out, many changes that can't be formulated as universal laws, and the laws are never truly exceptionless), but the idea of regular, universal sound change laws like this is still a very important tool in historical linguistics.
