I had such an issue with this my last pregnancy! The due date calculators gave me one date and my doctor gave me another. It turned out that both "thought" they were giving me a due date based on a gestation of 280 days (a calculated average gestation from LMP to spontaneous labor that doesn't take other factors into account, such as previous deliveries), but the doctor's office was using a manually read circular chart. The nurse didn't have it lined up quite right (my doctor noticed that when I asked), and it was a leap year, which the chart didn't account for. So after many months of fretting and looking this up, including all the due date calculation methods, I finally explained the two-day discrepancy!
I don't really care what my official due date is. I knew even with my first that she would be very late because my family takes longer than average to gestate babies (my aunt even had twins a week late, and they have an older sister!). But it was interesting to learn about different ways of calculating and satisfying to solve the mystery of why my EDDs were off even when they were using the same method to calculate it. Now my doctor's office uses a computer and I have just one EDD, which my doctor and I know is most likely quite a bit earlier than I will actually deliver.