In Hebrew, Shabbat/Shabbos, the Seventh Day, is a word spelled shin - bet - tav/sav. As one can see by even writing out the name of the final letter, there is a conflict in pronunciation. The final letter, tav/sav which is the last letter of the Hebrew alphabet, can be written with or without a dot (called a dagesh) inside. When it is written with a dagesh, it is agreed by all that its sound I like that of the letter “t.” When it is without a dagesh, however, the Ashkenazic tradition is to pronounce the letter like an “s,” while the Sephardic tradition maintains the solid “t” sound.
The tav/sav differential is not the only place where Sephardic and Ashkenazic pronunciation differ. For instance, the ayin is silent like the aleph in general Ashkenazic tradition, whereas the Sephardim make it a more guttural sound. And while the distinctions between Sephardic and Ashkenazic pronunciations are easily noted, one can also note that there are distinctive accents within each group as well (e.g. Chassidim).
Knowing the source for the different pronunciations of Shabbat verses Shabbos, however, leaves one with the question of why it is known in English as the Sabbath. Pronouncing the tav/sav as a “th” is common in the Yemenite tradition, which many linguists believe to be closest to the original Hebrew pronunciation.