There are lots of different types of “pills” related to pregnancy. It’s most helpful to break them into two categories:
Contraceptives PREVENT someone from becoming pregnant. 
Other types of pills are used when there is ALREADY an established pregnancy. It’s mifepristone, from this second group, whose FDA approval is currently being contested in the U.S. court system.
For all you nerds out there, here’s the detailed explanation of pill types and how they work:
Group : Contraceptives (“Contra” – against, “ception” – conception) are used to prevent pregnancy from happening in the first place. These include both typical birth control pills and emergency contraceptives. Contraceptives will NOT end an already established pregnancy. ALL of these types of pills are currently legal in all states in the U.S. 
The original or OG oral contraceptive, “The Pill” is available in many different formulations that go by various names. They are classified as Combined Hormonal Contraceptives (CHCs), because they all contain both an estrogen (usually ethinyl estradiol or estradiol) and a progestin. Progestins are compounds made in the lab that act in the body like progesterone. (Examples include levonorgestrel, norethindrone, drospirenone, and many others.) These progestins work to thicken the mucus in the cervix, preventing sperm from being able to swim up through it to reach an egg. Many CHCs also prevent the ovaries from releasing an egg. Therefore, all CHCs work to prevent sperm and egg from coming together (a process called fertilization). Without fertilization, there is no possible pregnancy.
Pills with just progestins are also available. These estrogen-free pills are safer for people with some medical conditions (such as migraine headaches with aura or a history of blood clots) and may have fewer side effects than CHCs. The “Mini-Pill” was the first type of these developed and uses a very low dose of progestin. A regular-dose progestin-only pill was also recently introduced, marketed in the U.S. as “Slynd”. These also prevent fertilization by thickening cervical mucus and/or preventing ovulation.
Emergency contraceptives (EC) are pills that also work to PREVENT pregnancy from occurring. Unlike the pills above that are taken daily, ECs are taken after intercourse has already occurred. Hence the nickname the “morning-after pill.” Since sperm are already well on their way, these types of pills work to delay release of an egg from the ovary (ovulation) if it has not already occurred. This delay gives time for many of the sperm to die off, so that hopefully by the time the egg is released (usually 1-3 days later), fewer sperm fit enough to fertilize the egg are still around.
There are two main categories of EC. The over-the-counter form (a.k.a. Plan B and many other brand names, active ingredient levonorgestrel), delays ovulation only. The prescription form of EC, called Ella (active ingredient ulipristal), not only delays ovulation but may potentially prevent a fertilized egg from attaching to the uterus, a process called implantation. Medically, a person is not considered pregnant until implantation has occurred, but there are some folks whose religious views may prevent them from using Ella for this reason.
Group : This category of pills is used AFTER someone is already pregnant or potentially pregnant. There are two medications in this category: misoprostol and mifepristone.
Misoprostol works to open the cervix and encourage the uterus to contract. It is commonly used to help bring on, or induce, labor in a pregnant person. It is also used to help people having miscarriages, as it can shorten the duration of their bleeding and reduce the risk of needing a surgery to clear out the uterus. Misoprostol has also long been used as a medication to cause an abortion, especially early in a pregnancy. Interestingly, misoprostol also has some effects on the stomach, and so it is sometimes used to treat stomach ulcers.
Mifepristone is the other medication in this category. It causes breakdown of the lining of the uterus. Using it together with misoprostol has improved the safety and effectiveness of both miscarriage treatment and medical abortions. Therefore, medical organizations currently recommend that they be used together for both situations.
Misoprostol and mifepristone taken together are also used as what is sometimes called “missed period pills,” in which a person who is late for their period (and potentially pregnant) takes them to “bring on” a period without first checking a pregnancy test. The legality of this approach in states that ban abortion is unclear.
Mifepristone is the drug whose availability in the U.S. has recently been called into question by a court case challenging the FDA’s approval of the drug. As the case makes its way through the Federal Appeals Court and, likely, the Supreme Court, mifepristone may become unavailable in the U.S. (even in those states where abortion is still legal). This would restrict access to the best standard of care for both early abortion and for miscarriages. Misoprostol alone can still be used, but it is slightly less effective than the combination with mifepristone.
Bottom line: Contraceptives, including The Pill and Emergency Contraception, work to prevent pregnancy and are not under legal challenge in the U.S. On the other hand, misoprostol and mifepristone are drugs used when someone is ending an existing pregnancy, either voluntarily (abortion) or not (i.e. miscarriage). Mifepristone is the one under legal challenge but still currently available in some states in the U.S.
Stay safe, stay well!
Those Nerdy Girls
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Additional Resources
TNG post on legality of emergency contraception
