Here in the US "grandma" (pronounced "gramma") is much more common. People might use "granny" in a funny / joking way. I think it's more common in the Southern and Western parts of the US. A famous "granny" from American comedy show was this lady: http://www.colettebaronreid.com/blog/featured/beverly-hillbillies-4th-chakra/comment-page-1/

No difference whatsoever. BTW "granny" (two n's)

Granny and grandma are shortened forms of the word Grandmother. Other English names used for grandmother are Nan and Nanna. Example: Tomorrow I will visit my granny/grandma/nan/nanna.