Why does Judaism celebrate Sabbath on Saturday and most Christians celebrate Sabbath on Sunday? When did most Christians (possibly excluding exceptions such as Seventh Day Adventists) and Jews start celebrating Sabbath on different days of the week and why?
To be clear, most Christians do not celebrate "The Sabbath" on Sunday. Strictly speaking, Christians do not celebrate the Sabbath at all* (although many Christians still refer to their "day of rest" as their "sabbath day", even though this has no direct relationship to the Jewish Sabbath.)  Christians traditionally celebrate on Sundays because this is the day Christ was raised from the grave.

I have not yet found a specific, authoritative reference for the fact that Christians worship on Sunday because that is when Christ was raised, but some references include here and here

*Apparently some Christian groups do call Sunday "the Sabbath" (with a capital S), but I believe this is a minority view out of ignorance of the significance of words, and is rarely considered dogma.