From my own experience growing up:
A Daddy: Is friendly with the children, wears boxers or Jeans after work in the evening, takes the children out for site seeing, eateries, celebrates your birthdays, sing songs with the children, buys things on way back from the office.

A Papa: Always keeps a long serious face in the house, ties wrapper after work in the evening, sees taking children out as waste of time and resources, you are the one that will remind him of your birthday, shuts the children down when dey are singing saying "you people are making noise", hardly buys anything for the children on the way back from work, kept a special cane somewhere to whip ur ass when ever u f-uck up.

Which is you father? A Daddy or a Papa?

Me dad is both....just dont mess with him

Daddy

Daddy=what those below 20 yrs called their father
Dad= what unmarried/newly married(above 20 yrs)call their father
Papa= what parents with grown up children call their own father.
This also applies to Mommy, mom, and Mama.
Note that Papa and Mama is usually looked at as more respectful by aged parents. Daddy, mommy, mom,dad is usually more suitable for young/younger parents. As a young parent i won't like my child calling me papa, but when i turn 50 something, i won't accept any other than Papa.
My Personal opinion. Not debateable. You are entitle to yours too.