Things like this can be highly family-specific. A friend of mine (German) says that in his family, his grandmothers are distinguished as "Oma" and "Omi". Which are both generic German words for any grandmother, but in his family, they are more specific. Like names. Another friend, they used "Oma" and "Großmutter" (a third generic word) to distinguish the two.
So there must certainly be families in the English-speaking world where kids commonly say "dad's dad" and "mom's dad". Even when unlike in Scandinavian languages, it's not the canonical form.
I think it's more common to call them Grandma and Grandpa Lastname or Grandma Firstname and Grandpa Firstname. I've also seen it where one set of grandparents are Grandma and Grandpa and the other set is Nana and Papa or Mimi and Pop Pop or whatever set of less formal terms they use for the relations.
I'm not sure I've met anyone who doesn't have more familiar terms than dad's mom and mom's mom. They're probably out there, but not super common.
So there must certainly be families in the English-speaking world where kids commonly say "dad's dad" and "mom's dad". Even when unlike in Scandinavian languages, it's not the canonical form.