할머니(hal-meo-ni, halmeoni)
A general term for grandmother used among family or close relations
When to use
family casual talk, friendly family gatherings, children calling grandmother
The nuance
Used when addressing or referring to one's grandmother in a familiar or family context. It is casual and comfortable language.
할머님(hal-meo-nim, halmeonim)
An honorific form of grandmother expressing respect and politeness
When to use
formal occasions, expressing respect, referring to someone else's grandmother politely
The nuance
Used in formal situations, to show respect, or when referring politely to someone else's grandmother.