There are several types of twins. The type of twin pregnancy depend on whether it results from one egg or two, and if one egg, depending on when the embryo splits. Twins that result from one fertilized egg are called monozygotic twins and twins from two fertilized eggs are called dizygotic twins.
All dizygotic twins have two placentas; this is called dichorionic. They also have two internal compartments (amniotic sacs) which is called diamniotic. They are also called fraternal twins.
Monozygotic twins that split very early will also be dichorionic-diamniotic but they will be identical since they came from the same embryo. However, if they split a bit later, they may have only one placenta; this is called monochorionic. Monochorionic twins can also be diamniotic with a dividing membrane between the two fetuses but they can also have no dividing membrane; this is called monoamniotic.
All types of twin pregnancies are at an increased risk for essentially every complication of pregnancy, including preterm birth, gestational diabetes, hypertensive disorders of pregnancy such as gestational hypertension or preeclampsia, and of course more aches and pains and all of the other joys of pregnancy. Monochorionic pregnancies, however, have some special risks including a risk for twin-to-twin transfusion syndrome (TETS) for monochorionic-diamniotic twins and a risk of cord entanglement for monochorionic-monoamniotic twins. Because of this, monochorionic twins are much higher risk than dichorionic twins and require significantly more testing.
Most twin pregnancies can still be delivered vaginally as long as the first twin is head down. The one important exception to this is monochorionic-monoamniotic twins; because of cord entanglement, these pregnancies need to be delivered by Cesarean delivery.