adding to the above,
it is important to note that these distinctions come into play when examining the operation of the price mechanism.
when you have the operation of free market demand and supply, prive firms often supply too much to the market. why? because they only take into account the private costs - the direct costs that the firm incurs, eg labour costs, cost of rent, etc.
the social cost is equal to the private cost PLUS the cost of any negative externality present. it takes into account the costs borne by society eg pollution, resource depletion. the price mechanism fails to account for this cost, and hence resources tend to be overused and underpriced.