a community is a group of people living together or sharing interests in the wider society. the elderly community, the gay community. Police working with community relations work with a particular neighbourhood. Society is a broader term- societal problems would apply all over the country. However a criminal can be a menace to society or a menace to the community. I suppose it depends what the speaker has in mind but basically society is wider.' Modern society is facing many problems including a breakdown in the sense of community.'

Society usually means the wider culture, whereas community is a smaller group of people. So for example: You have American society, which the larger culture and beliefs of America as a country. But your town is a community, your school is a community, etc. Communities are affected by society's beliefs and problems, but they have their own traditions and problems as well. I hope this is helpful :)