שים / תן חלקנו בתורתך

Question

I've noticed that on Yom Tov, sefardi (edot mizrach) machzorim say תן but on Shabbat in siddurim, they say שים in the bracha of Yom Tov/Shabbat respectively (which are parallel).

Am I just not widely read enough, and this is actually nothing to do with Yom Tov and Shabbat, but happens to be something to do with nusach/minhag/girsa among the different siddurim/machzorim I've used all my life? Or is there something in it i.e. one is more appropriate for Shabbat and and one for Yom Tov? If so, what the lesson?

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^{I have occasionally noticed שים used on a Yom Tov (usually in a Siddur, not a machzor, so could be a copy/paste artefact - such as when you see יום טוב in brackets as if it is not always applicable on the non-musaf שלש רגלים amidahs, because they are clearly copy/pasted from the musaf one and didn't remove the brackets), but never תן in a Siddur on Shabbat.}

^{I don't think I've ever seen שים in an ashkenazi siddur but I try to avoid them as I am sefardi.}

Answer 1

The reason we don’t say ״מקדש ישראל והשבת” - unlike Yom Tov, where we say מקדש ישראל והזמנים״” - is because Shabbos is holy on it’s own, and doesn’t need the Supreme Court to sanctify it like by Yom Tov

So perhaps we can say that this is the reason for this difference as well - being that we find that the term ״שים״ is used for something that does not come as a reward for our actions, but rather a gift from above - like we find in Shemoneh Esreh, where we say: “ותן שכר טוב לכל הבוטחים בשמך באמת” - for those who deserve reward we use the term “ותן”, and for the rest we say: “ושים חלקנו עמהם”