You are all going to hate me for this, but when I was growing up nannies were lovely cuddly people who were "hired" to take care of small children. So, in order to differentiate between the strict but wonderful Nanny, we called our grandparents Granny or Grandpa (or a variation on the theme). My own parents didn't have a nanny, but sometimes my grandmother (Granny) asked my mother's old nanny (well, old to us) to help her look after us when we stayed with her (and Grandpa, who I called Poopa).
My husband and his brothers were also brought up by nannies (before and during the War) so the word "Nanny" has always been associated with a beloved woman who did a huge amount of childcare. Mother, on the other hand, was a rather distant and glamorous figure who wafted in and out of small children's lives. And, later on, became Grandma.
Anyway, it's now 2015, and I'm Granny and my husband is Papa (pronounced Poppa). The grandchildren think it's hysterical that I used to call my grandfather Poopa. I suppose it was a bit odd, but he didn't mind a bit. It's not what you call them. It's how much you love them (and vice versa).