Most people use the phrase "common good" as if it were a synonym for the general welfare. There are two common goods, but in different senses of that word. In Latin they are called bonum commune hominis and bonum commune communitatis.
The first of these is identical in meaning with happiness. It is common in the sense that it is the same in essence among all human beings. (See the entry under Happiness.) When I say it is the same in essence for all human beings, it may differ from individual to individual only in accidental respects and in degree.
The other, the bonum commume communitatis, or the good of the social community is a means, not an end. It is common in the sense that all individuals, in their pursuit of happiness, must employ it as a means to that end.
This means to happiness is common in the sense that human beings share in it. They should all aim at it, each individual according to the individual differences that differentiate them.
For example, the peace of the society is an aspect of the common good of the community everyone should act to procure a peaceful community. Another aspect of the community's good is justice in the treatment of society's members. Each individual should work to procure justice for all, so, too, liberty for all the equality of all.