Polite and affectionate term for one's own grandmother or an elderly woman addressed as a grandmother figure. Often used by children and in family contexts.
See also: ばあさん
My grandmother takes a walk in the park every morning.
おばあさん、このお菓子をどうぞ。
Grandma, please have this sweet.
old woman; elderly lady
Refers to an elderly woman in general, not necessarily a relative. Can be used politely or affectionately, but context matters to avoid sounding patronizing.
See also: ばあさん
道でおばあさんが重い荷物を持っていたので、手伝った。
An old woman was carrying heavy bags on the street, so I helped her.
On the weekend I'm going to visit my grandmother in the countryside.
A little girl was walking, leading the old woman by the hand.
おばあちゃん is the intimate, childish term used within the family, while おばあさん is the more polite, standard word used to address or refer to elderly women respectfully.
お婆さん adds the honorific お and is the more polite, commonly used form, while 婆さん alone sounds blunter or more familiar.
おばあさん is the standard, polite word for an elderly woman or grandmother, while 婆ちゃん is a casual, affectionate term used mainly within the family or by children.