μπ makes a b sound, babas

As for the history -

The word μπαμπάς comes from the Turkish word for father, in one version of ancient Greek (koine) the word that was used primarily was πατέρας and παπά, but παπά came to mean priest (παπάς) so the language changed. Katherevoursa never got rid of μπαμπάς or really common words like φαντάρους (latin) for στρατιώτης (greek) which means soldier or πουτάνα (latin) for πόρνη (greek) which means prostitute.

Hi, Sarah.

The truth is they are two totally different words BUT if you heard someone pronouncing them the same, then don't trust him/her anymore if he/she tells you they know Greek.

The words you are referring to are "μπαμπάς" = dad & "παπάς" = priest

Like Θεόδωρος wisely wrote, you could also find the word father = πατέρας

However, in no way are these two words the same. 

Also baba might come from Αββά which is a semitic word for dad

ευχαριστω παρα πολυ Θεόδωρος, Πολυ σαφής :)