You can be a culture. You can build on the experiences of the past and spontaneously continue the culture in your own original way. A society will by its very definition resist change. Culture is a force of change in itself. Society is the sum of those relations that are under some form of public constraint.
Society consists of what people do because of necessity, because they have to.
A society is bounded temporarily and spatially. Members of a society are only those who live within its boundaries and agree to the validity of its rules. Culture is whatever we do with each other by undirected choice. A culture is not bounded. Anybody at any time anywhere can participate in a culture.