The NIPT is a relatively new test (since the Fishparents were born, anyways) that tests mostly for common trisomy defects. The NIPT is taken and run between 10 and 14 weeks of pregnancy, because at that point the placenta is hooked up to the pregnant person's blood supply, and the baby's blood/DNA will be in the pregnant person's blood. Several companies have proprietary technology that will take the pregnant person's blood, filter out the baby's DNA and run screenings on it.
The NIPT can't tell you for 100% sure if there are issues. It's a screening test, which means it will give you a result like "low risk" or "high risk" for problems. If you get a "low risk" result, you can be pretty confident it's correct. If you get a "high risk" result, it's less certain. If you do get a high-risk result, your doctor will recommend other tests with higher accuracy rates.
The NIPT is really popular with doctors, since it's a non-invasive way to get good information about the baby, and it's popular with parents because it can tell you the sex of your baby earlier than the 20-week anatomy scan. It can take a week or more to get the results back, depending on which company is processing your blood.
The NIPT tests for chromosomal disorders caused by extra or missing copies of a chromosome. It looks for Trisomy 21 (Down syndrome - caused by an extra chromosome 21), Trisomy 18 (Edwards syndrome - caused by an extra chromosome 18), Trisomy 13 (Patau syndrome - caused by an extra chromosome 13). The NIPT will also test for missing or extra copies of the X and Y chromosomes (Fragile X syndrome, Turner syndrome, Klinefelter syndrome, Triple X syndrome...) Some of these syndromes can have severe effects on the baby and some don't have very good odds of survival once the baby is born. The accuracy of the NIPT varies for each syndrome it tests for (for trisomies 21, 18 and 13, the accuracy is very good, but for other things there's a slightly higher risk of false-positives and false-negatives).
Your results may include a "fetal fraction" percentage, or you might get a result of "incomplete fetal fraction". This just means that there wasn't enough of your baby's DNA in your blood sample to run the tests. In most cases, this is just because the test was ordered too early in your pregnancy and the placenta wasn't developed enough to get enough of baby's blood in your system.
The Nuchal Translucency scan is another way to screen for chromosomal abnormalities and heart defects. Like the NIPT, the NT scan is a screening test, meaning you'll get a result like "low-risk" or "high-risk" - the test can't actually tell for 100% sure if your baby has chromosomal problems. The NT scan is usually done between 11 and 14 weeks of pregnancy.
The NT test comes in two parts. There's a blood-testing part and an ultrasound part. The blood test will test you for the amounts of pregnancy-associated plasma protein-A (PAPP-A) and human chorionic gonadotropin in your blood. Then you'll get an ultrasound of your baby to measure the amount of fluid at the back of the baby's neck. The blood test and the measurements of the baby are combined to give you the result.
In a baby with chromosomal abnormalities or heart defects, there's more fluid than normal at the back of their neck, and your blood may show elevated levels of the PAPP-A protein. If you get a high-risk result on the NT scan, your doctor will probably recommend you get a diagnostic test to know for sure.
As the NIPT gets more popular and widely-used, the NT scan is getting less popular and less widely-used. The Fishparents weren't even offered it as an option for Fish, since the NIPT gives the same screening results and may be more accurate.
A high-risk result on the NT scan does not for sure mean that your baby has a chromosomal or heart abnormality. Depending on your personality, hopes and dreams, realistic life expectations, etc, you may choose to get a diagnostic test like CVS or amnio to know exactly what's going on with baby, but if those sound too invasive, many people who get high-risk screening results go on to have healthy babies.
Unlike NIPT or the NT scan, CVS is a diagnostic test, which means the results you get are pretty ding dang accurate. The test is done by collecting a sample of the chorionic villi, which are little projections (tiny tentacles) on the placental membranes. These villi are part of the border between your blood and baby's blood, so they're a prime carrier of baby's DNA.
The tissue sample can be taken two ways - either a catheter is put through your cervix into the placenta, or a needle is put through the belly and uterus into the placenta. CVS is usually done between 10 and 12 weeks. CVS can test for around 200 different genetic abnormalities, so it can give you a pretty broad picture of baby's genetic situation!
CVS does not test for neural tube defects, so if you decide to get CVS and want to know about any neural tube defects (like spina bifida), there are blood tests you can get that will check for those.
Because CVS involves needles or catheters sticking into the uterus, there are some risks to having it done. There are small risks of miscarriage, amniotic fluid leaking and infection.
A helpful link with good information about CVS is here: Johns Hopkins Medicine - CVS