grandmother vs gran

grandmother and gran both are nouns.

Word	Noun	Adjective	Verb	Adverb
grandmother	Yes	No	No	No
gran	Yes	No	No	No

As nouns, grandmother and gran are synonyms defined as:

Other synonyms of grandmother include grandma, grannie, granny, nan, nanna.

grandmother (noun)	gran (noun)
the mother of your father or mother	the mother of your father or mother