Identical twins - one egg + 1 sperm that splits into two after fertilization aka clones. This happens randomly in the population.

Fraternal twin - Two different eggs + 2 different sperm from daddy. They are siblings that happen to share a uterus. This genetic in some families.

Semi-identical twins - One egg + 2 sperm. The egg splits before it is fertilized. The genetically identical eggs are fertilized by different sperm. Freaky huh....