Monozygotic twins are identical twins that develop from a single fertilized egg that splits into two embryos with a shared placenta. Dizygotic twins are fraternal twins that come from two separate eggs fertilized by two different sperm, with separate placentas.

Identical twins are classified by how they share the placenta and the surrounding sacs, since these structures determine pregnancy type and risk.
The placenta develops from the chorion, which is the outer membrane of the embryo. The amnion is the inner sac that surrounds the fetus and holds the amniotic fluid. Monozygotic twins may share or have separate placentas (monochorionic or dichorionic) and may share or have separate amniotic sacs (monoamniotic or diamniotic). For simplicity, I will refer to the chorion as the placenta, but the placenta forms later from the chorion along with other maternal tissues.
The figure below shows the main types:

- Single fetus: One placenta and one amniotic sac, which is the typical structure in a singleton pregnancy.
- Monochorionic monoamniotic (mono/mono or MoMo) twins: Identical twins that share both a placenta and an amniotic sac. This is rare and higher risk because the cords can become entangled, and rare cases can result in conjoined twins.
- Monochorionic diamniotic (mono/di or MoDi) twins: Identical twins that share a single placenta but each has its own amniotic sac. This is the most common type of identical twin pregnancy.
- Dichorionic diamniotic (di/di or DiDi) twins: Twins with separate placentas and separate sacs. This includes all fraternal (dizygotic) twins and some identical twins that split very early. It is the lowest-risk twin arrangement.