Is the social the same as society?

In the Social Sciences a social group has been defined as two or more humans who interact with one another, share similar characteristics and collectively have a sense of unity.

A society, or a human society, is a group of people related to each other through persistent relations, or a large social grouping sharing the same geographical or virtual territory, subject to the same political authority and dominant cultural expectations. Human societies are characterized by patterns of relationships (social relations) between individuals who share a distinctive culture and institutions; a given society may be described as the sum total of such relationships among its constituent members. In the social sciences, a larger society often evinces stratification and/or dominance patterns in subgroups.

A society can be viewed as a large social group.