The problem is that people think that with a test they are guaranteed a "normal" baby. A test like Harmony/NIPT actually only looks at 4 pairs of chromosomes: 13,17 and 21 (if I am not mistaken in numbers) and sex chromosomes. If there is a larger concentration of one of the 3 sets of chromosomes in the mother's blood, this could mean a problem in baby. If they detect a Y chromosome the baby is a boy (amazing to think that as a woman you might actually have a chromosome circulating: maybe that is the cause of "pregnancy dementia"
, could be interesting to compare women carrying boys and girls
). Any other problem (like deletion of part of a chromosome, or even a mosaic, meaning that there are both normal and abnormal cells) are not detected. Sex chromosome abnormalities (like Klinefelters) are not always detected. What the test does is (try to) detect foetal DNA strands in the mother's blood, so not complete cells with a nucleus. The frequency of certain bits are compared to each other, and a large difference in concentrations might mean there is a problem (= high risk result). Then the advice usually is to go for a more invasive test (taking some amniotic fluid or a "placental biopsy") to really have foetal cells to analyse more accurately. This should only be done if you do consider a termination, as both come with a risk of miscarriage.
PGD takes one (or a couple) of cells from an embryo before it is transferred. As the tests take some time, the embryo's are usually frozen afterwards, and a FET is done once the results are known. PGD can also damage the embryo, causing it not to survive. PGD can test for much more problems, but it is usually only done if the future parents carry a known genetic mutation (eg cystic fibrosis, sickle-cell,...). I did not know it also was used to screen embryo's without a known genetic problem.