By this shitty definition do you want to say there is also a mother and Mommy? Or is it Mother and Mom?
This is the definition you need to have in your brain as from now
Father/Mother- is a biological relation. It has to be your biological Male or Female parent to be a father or Mother
Dad/Mom - this is the relationship based in role. If i play a father figure to someone else’s kid then i Am a Dad and not a Father.
i.e Daughter: Mom can i travel to see Mother this weekend?
Daddy/ Mommy - This is often used to describe lovers or love interests.
i.e: male: who’s your Dady
Female: You, you, now F***k me Harder DADDY