The Rambam Laws of Shemita (chapter 10 law 2) writes that 2503 was the first year of counting shemita, but then says that shemita (year 7) was in 2510. He further gives other dates for shemitah that are one year off of the rabbinic count. The Rambam explains that the first year of Adam is counted as the second year of the creation. Rambam thereby adds one year on the rabbinic count.
One idea is to count the time before Adam’s creation as the first year. But there is a more compelling reason. Birth years are traditionally year zero. Furthermore, Abraham was 99 when Ishmael was 13 (Bereishit 17:24-25), and Abraham was 86 when Ishmael was born (Bereishit 16:16). Ishmael’s birth year is therefore year zero.
The rabbinic count similarly has all birth years as year zero, and the year of Adam’s birth also starts with year zero. Rambam’s addition of one year treats year one of Adam as year two, year zero (birth year) of Adam as year one, and the time before Adam as year zero
The halachic authorities add one year to Rashi’s shemita and one year to the halachic shemita. Halacha considers 3829 the first year of shemita, but we call it 3830. 3829 is 69 common era, which we call 70. Rashi’s shemita can also be aligned with the halacha by assuming a two year shift, counting year zero as year one and then counting the time before Adam’s birth as year one.