The Jewish Encyclopedia explains that the difference in the calculations is based on an argument as to when the first year of the first cycle began when the Bnai Yisrael entered the land under Yehoshua. It should also be noted that the calculation also depends on how the Yovel (Jubilee) year enters into the calculation. Is the fiftieth year a separate year so that the first year of the next Shmittah cycle is year 51 or is the first year of the next shmittah cycle the yovel year as well (year 50). Note that the citation below says that 850 years was an even 17 cycles so that it is assumed that the Yovel is year 50 and the new cycle starts in year 51. Thus 17*50=850.
The Talmud states that the cycle started in the year 2503, while the Samaritans state that the cycle started in 2794 for a difference of 291 years. If the seven year cycle is used this leads to 41 (seven year) cycles and a remainder (difference) of 4 years. If the Yovel cycle is treated as 50 years as below then the difference of 291 years is 5 yovel cycles and 41 years which is 5 shemittah cycles and 6 years. This makes the Samaritan cycle one year off from the Talmudic cycle.
Note that if one uses 49 years and the other 50 years, the result becomes complicated. Additionally, if the calculation after the destruction of the second temple changes from 50 years to 49 years, that could make a difference unless both changed in the same way.
Talmudic and Samaritan Calculation of Jubilees.
The exact year of the shemiṭṭah is in dispute, and different dates are
given. According to Talmudic calculations the entrance of the
Israelites into Palestine occurred in the year of Creation 2489, and
850 years, or seventeen jubilees, passed between that date and the
destruction of the First Temple. The first cycle commenced after the
conquest of the land and its distribution among the tribes, which,
occupied fourteen years (which would be 2503), and the last jubilee
occurred on the "tenth
day of the month [Tishri], in the fourteenth year after that the city
was smitten" (Ezek. xl. 1), which was the New-Year's Day of the
jubilee ('Ab. Zarah 9b; 'Ar. 11b-12b). Joshua celebrated the first
jubilee, and died just before the second (Seder 'Olam R., ed. Ratner,
xi. 24b-25b, xxx. 69b, Wilna, 1895).
The Samaritans in their "Book of Joshua" date the first month of the
first Sabbatical cycle and of the first jubilee cycle as beginning
with the crossing of the Jordan and the entrance of the Israelites
into their possession; and they insist that the date was 2794 of
Creation, according to the chronology of the Torah "and the true
reckoning known to the sages since the Flood" ("Karme Shomeron," ed.
Raphael Kirchheim, § 15, p. 63, Frankfort-on-the-Main, 1851).
