“Societal” more specifically refers to a society, whereas “social” can refer to the relationships between people in general. And “involve” is more active than “include”—“include” just means to make something a part of something, while “involve” is to add something to the action or process

'Social' refers to relationships between people or groups within a society, while 'societal' has to do with society as whole. 'Societal' is used more in academic contexts and not really in colloquial/ conversational context. (So I would probably use social issue). To 'involve' something implies that the object or action takes an inseparable/integral part. To 'include' implies that the object is part of the greater group or whole.