Hmmm. I had two Nanas, Little Nana ('cause she wasn't very big), and Big Nana ('cause she was tall). I didn't really know Little Nana as she died when I was five, but Big Nana was a significant person in my life until her death in the 1980s.
Nowadays, my mum is Nana to my boys and hubby's mum is Granny. Nana is much more with it and dynamic - a real good laugh - whereas Granny is self-pitying old lady reminiscent of Hyacinth Bucket on Prozac.
My eldest is insisting on my being 'Gran' when he and his wife eventually reproduce, but I've told him no-way. I don't want to be Nana, either. I think the Kumars call their granny 'Ummy' or some such, which would suit me fine.