As you probably know "social" has a wide range of meanings: social networking, social media, social event (eg a party), a social person (someone who enjoys being around people and making new friends). It also can be used to describe things that relate to society in general: a social problem, for example, is an issue that affects most of society or is caused by something in society, for example gun violence in the US.
"Societal" has a very narrow range of meanings. It pretty much only has one meaning, which is similar to the last meaning of "social" given above. The Oxford Advanced Learner's Dictionary defines it as: "connected with society and the way it is organized." It is a technical word for academic writing, not something we use in conversation very often.