Refers to one's own grandfather or someone else's grandfather. The kanji お祖父さん is sometimes used for this meaning.
My grandfather goes for a walk every morning.
That child wrote a letter to their grandfather.
elderly man; old man
A respectful or affectionate term for an elderly man, not necessarily related. The kanji お爺さん is sometimes used for this meaning.
An old man was playing shogi in the park.
A kind elderly man gave me directions.
The old man in my neighborhood often greets me.
During summer vacation I went to my grandpa and grandma's house.
おじいさん is the polite, standard way to refer to an elderly man or grandfather, while 爺 is casual and can sound rough or derogatory.
おじいさん is the polite register form used to address or refer to a grandfather or elderly man, whereas じいちゃん is the casual, affectionate family register.