No. 38 weeks from conception is only an estimate of when a woman will give birth. The vast majority of full-term births occur between 36 and 40 weeks from conception, with only a small percentage actually being at exactly 38 weeks. A woman who gives birth two weeks past her due date has probably not miscalculated, but rather has a strong placenta (and a stubborn baby)!
Pregnancies going more than two weeks past the woman's due date (as assessed either by an early ultrasound or according to the woman's last menstrual period) are considered higher risk and therefore most doctors choose to induce labor - causing the woman to go into labor and give birth to her child. This is performed in several different ways, depending on each individual case.
Although induction is often associated with stronger, less effective contractions, this is not always the case. To avoid induction, a woman may choose to see her ob/gyn and ask to have her membranes stripped. This is generally only possible when there is at least some level of dilation and therefore is not an option available to all women. Stripping of membranes, particularly when the cervix is only slightly dilated, can be very painful. It can, however, sometimes enable the woman to labor mostly at home, in her natural surroundings. Such a labor often proves to be more comfortable and less stressful.