'baba' originates from Slavic languages, specifically the Polish and related Slavic word 'baba', where 'baba' meant 'old woman' or 'grandmother'. The pastry sense is linked to Polish 'babka' (a small cake); in a separate sense, the honorific 'Baba' comes from Persian/Arabic 'bābā', meaning 'father' or 'respected elder'.

'baba' in Slavic languages remained 'baba' (Old Russian, Polish) and entered English as a colloquial term for 'grandmother'. The pastry meaning developed from Polish 'babka' (diminutive) into French 'baba' (as in 'baba au rhum') and then into English. The honorific sense passed from Persian/Arabic 'bābā' into South Asian usage and was adopted into English through contact.

Initially, in Slavic it meant 'old woman' and in Persian/Arabic it meant 'father' or 'respected elder'. Over time English adopted the Slavic sense as an affectionate term for 'grandmother', borrowed the pastry name from Polish/French, and retained the honorific sense in cultural/religious contexts.