iacisrmma, Halachic leap years. (Secular leap years were devised by Pope Gregory – hence the Gregorian Calendar. Gregory was once asked why they (the Catholics) don’t just adopt the Jewish calendar which is known to be in sync with both the sun and the moon. His famous reply “Better to be wrong with the sun than right with the Jews”.)
I haven’t seen Rabbi Heber’s article, but in very short; Shmuel’s tekufa is based on a more simple calculation, which is inaccurate, but is still used to calculate only birkas hachama. R’ Adda’s tekufa is more complex and therefore more accurate, and therefore used to add months to a Jewish leap year. They both probably started off at the same point, but are now weeks apart.