If you’d search in the dictionary for papi you’d probably see that it means “dad” or “father”. Yes, it’s your old man, but using it in that context would be a pretty weird. Why? It’s simple: papi is – nowadays at least – more used to say “darling” or “sweetheart”, in most parts of Latin-America at least.
In Spain it’s still used to say “daddy”. And while many people in Latin-America use it as a synonym for cariño or cielo, it’s still a bit sexist. Mami is no difference; it can mean “mommy” (mainly in Spain), but above all “sweetheart” (in a bit sexist way, in Latin-America).
Spanish Word of the Day: acá
Spanish Word of the Day: coño
Spanish Word of the Day: chulo
Spanish Word of the Day: gringo
Spanish Word of the Day: colega