There are two types of twins: monozygote and dizygote. The first one originates from one egg and one sperm like missy told. A dizygote twin are two fertilized eggs like any other normal siblings, only now in one pregnancy. Therefore dizygote twins always have their own placenta, amnion and chorion. Monozygote twins can have all forms:
- seperate chorion (therefore also seperate amnion) (dichorionic diamniotic)
- shared chorion but separate amnion (monochorionic diamniotic) and
- shared amnion (and therefore also shared chorion) (monochorionic monoamniotic).
It's no coincidence one monozygote twin will share its amnion or not, it all depends on the moment the embryo divides. The earlyer this happens, the less the babies share. If the embryo tries to divide after 14 days, you get a siamese twin. TTTS (twin to twin transfusion syndrome) only occurs in monozygote twins.
After the twin is born you often can't tell the difference between monochorionic diamniotic and dichorionic placenta. The pathologist injects some fluid through the veins to see if the veins go from one side of the middle membrane to the other. If so, it's a monochorionic twin.

I just love the twin subject