When I was growing up, it was pretty standard (or for our region). I called one set of grandparents Granny and Grandaddy, and the other set Grandmother and Grandaddy. We didn’t really have a relationship with our great grandparents because only one was still living. I read an interesting article (This one? or maybe this one? Probably both) about what children call their baby boomer grandparents.
Patrick and I sort of let the grandparents decide what to be called, but I’m pretty sure I dictated it to my parents. Since I liked calling my grandparents Grandaddy and Granny, that’s what my parents got. Nana and PopPop already had some grand children calling them those names, so they stuck with it. Grandude and Grandma also chose their names. Sometimes people laugh about Grandude, but the boys love it and it allows them to draw out the long u sound.
It’s fun though, when you have names for people that weren’t really thought of in advance. I don’t know why it didn’t occur to me that it would be confusing for the boys if my mom’s mom, my mom, and I were all in the house at the same time. “Mom” “Granny” could be either of them at different times. Confusing! So we had to come up with a name for my granny. Great Granny was logical, but a mouthful (no more so than Grandaddy, suppose, but still awkward). We organically went toward GiGi (GG). I know! So creative! Who would have thought? (Just kidding. I realize this is not creative at all.) It’s really helped though because it gives the boys a memorable name for her and a way to talk about her when she’s not around. It also helps them process the generational questions of who is whose mama and dada as we go up the family tree. We also have Great Nan and Old Grandad (if you know the bourbon of the same name, you’ll understand why this is funny).
Many of our friends use different names. People used to pretty reliably ask kids, “Oh are you going to Grandma’s” and expect the kid to know what they were talking about–now people have all kinds of names reflecting heritage, preference, and the never aging boomers. What do you use and why?
Academic Leigh Speaking 
My step-kids come from a long tradition of Grandma & Grandpa in Elena’s family, both in Albuquerque & Belen. When Miguel came along and was designated by Celena, his mother, & Elena as my grandson rather than step-grandson, I just naturally became Grandpa. Tom, Celena’s father, wasn’t around much at that point. When he was visiting a year later, having another “Grandpa” around became confusing for Miguel. Since I could see that Celena would prefer the more traditional name for her father, I opted for “Grandad,” This was a more natural version of the name my niece & nephew used for my father. (They actually called him “Dan-dad” because that’s what Liz could manage when she started talking.) Tom has since evolved into Grandpa Tom. I told Miguel it was okay for him to call “Grandpa” a few years ago. He thought about it for a minute and then said, “No.” BTW, my mother was always Mother and GrandMother. No exceptions.
All of my grandparents were Grandma and Grandpa (I have three sets), and we differentiated them by adding the last name when we talked about them, ie Grandma Alley vs Grandma Funk. My mom and dad chose to be called Grammy and Gramps. When I become a grandmother, I’d like me and Michael to be Oma and Opa, which is what Michael calls his grandparents due to their German heritage.