Is there a need for both, or should they be merged/synonimized?
Speaking from an academic perspective, these two words have totally different meanings. Society refers more to social structures and organization, while culture is shared history and identity. Culture would impact the form of a society, but the two terms are in no way synonyms.
For example, if you wanted to ask about class structure, society would fit, while culture would likely be inappropriate unless the form of the class structure was highly impacted by some specific tradition (such as caste systems). Similarly, asking about the development of an art tradition would fall under culture and likely not society. The main difference is that culture has an element of identity, while society is collective and systematic.
I think the confusion might be from the generality of the current definition of the society tag. It's accurate, but rather broad and lacking any examples. The tricky bit is that the terms overlap fairly heavily in meaning, but not in usage.