Both are grandmothers but the first ( babaanne ) is the mother of your father and the second ( anneanne) is the mother of your mom.

Both of them are grandmothers, Turkish people have separated them in two ways as "babaanne" who is father's mother and "anneanne" who is mother's mother. But on the other hand, personally, as a Turkish person, I call my parents' mothers at the same way like europeans by calling them "grandmother".

thank you : )

babaanne=My father's mother anneanne=My mother's mother :)