Doctor's break down trimesters different too. When you reach past 40 weeks you are considered "overdue" and in your 10th month of pregnancy. This is the "2 week" span that helps doctor's give more time since the exact date of conception and implantation varies so much. This is why they date your due date by last menstrual period. This assumes a regular 28 day cycle with ovulation occurring on day 14 of the cycle. Women that have longer cycles may need this "extra" baking period for their babies because she may not really be "due" because her dates were calculated by a 28 cycle.
Every week you are at plus 1 day you are in the following week and complete it by the end of that week. If that makes sense lol. For example: 38 weeks and 1 day is your 39th week of pregnancy, completed at 40 weeks ;).
You are in your 9th month. At 36 weeks you have completed your 8th month. 37-40 is your 9th month of pregnancy. You complete your 9th month term at 40 weeks :).