International mostly means something (a company, language, or organization) involving more than a single country. The term international as a word means involvement of, interaction between or encompassing more than one nation, or generally beyond national boundaries. For example, international law, which is applied by more than one country and usually everywhere on Earth, and international language which is a language spoken by residents of more than one country.
A society is a group of individuals involved in persistent social interaction, or a large social group sharing the same geographical or social territory, typically subject to the same political authority and dominant cultural expectations. 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 of members. In the social sciences, a larger society often evinces stratification or dominance patterns in subgroups.
Heav'n forming each on other to depend, A master, or a servant, or a friend, Bids each on other for assistance call, Till one man's weakness grows the strength of all.
Alexander Pope, An Essay on Man (1733–34), Epistle II, line 249.