Every family I have ever encountered using English as the medium of communication has had a different term for both maternal and paternal grandparents. There would not be an absolute answer to your question, as a multitude of variables abound in the field of sociolinguistics.
Dialects and regional differences vary according to the surrounding culture and their etymology. Grammatically, a morpheme, either a suffix or a prefix, would be utilized to indicate a diminutive.
Linguistic extrapolations could be made analyzing both cognitive and phonetic development in infants: at such a young age, they would be learning about the relationship to their grandparents and the concept of diminutives. Such a diminutive would distinguish between paternal and maternal relationships. Given that an infant is not ready to produce "maternal grandfather", bilabial allophones could phonetically surround a vowel, as in your example of "Pop-pop".
This reasoning suffices for all of the linguistic manifestations that I have ever encountered. As soon as the extended family agreed upon and accepted such a childish morpheme, the phenomenon would forever fossilize into the child's linguistic inventory.
Eric Paul Monroe