The Italian word for 'grandpa' is nonno and comes from the Latin root nonnus which appears in Late Latin (a term used to describe the written Latin of the 3rd to 6th centuries AD) and is possibly derived from colloquial child's speak.
The word originally referred to monks, but developed to mean a scholar or elder, and eventually to refer to older men in general.
In Italian there is no differentiation between paternal and maternal granddads, and a great grandfather would be referred to as bis-nonno.
A secondary use of the word nonno in Italian appears in military 'jargon' where it refers to a soldier who has served most of his draft period.
