What is the difference between a Father and a Dad?

A father is the man who got your mother pregnant. He doesn't become a dad until he is there for you and you become his entire world and everything he does is for you.

Father is used if you not that emotionally attached to him, dad is used when you have more emotional attachment. The saying, "anyone can be a father, but one person can be a dad." You can have a father figure in your life and not care about him, he's only a dad when there's a lot of dad and child bonding time.

Cory_the_Overlord is right

Father is biological usually
Dad is basically just your mother's husband