Yom Shabath is Saturday -- actually, Friday sundown to Saturday sundown, since the day starts at sundown. So Sunday is being treated as if it were the Sabbath, but it's being observed on a different day.
No clear reason for the shift from the Sabbath to the Sun's Day. The assimilation of pagan traditions as the new religion spread was doubtless an influence, for the same reason that Christian tradition attached Christmas to the Winter Solstice. OP's suggestion that it was to commemorate the day of the Resurrection could be another.
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