Kenan Malik in Pandaemonium:
These are all phrases that seem indispensible, phrases which we all use, and of which we have an instinctive understanding, yet the meanings of which are all contested and seemingly impossible to define.
These phrases are often used interchangeably. Many philosophers and political thinkers would argue, however, that there are fundamental differences in their meanings. In the ‘common good’, ‘common’ implies commonality among all individuals that belong to a certain group, whereas in ‘public good’, ‘public’ usually refers to matters that are subject to collective action. In contrast to the term ‘good’, which often signifies moral ends that people ought to pursue, ‘interest’ is frequently associated with material benefits. And so on.
I am going to ignore most of these debates about the distinct meanings. What I want to concentrate on is a more fundamental issue that all these concepts attempt to grasp: the relationship between the individual and society, and of the way in which the good of individuals relates to that of a larger whole. I will use the phrase ‘the common good’ to refer to that broad sense of the good of the larger community or society.
More here.