What you describe i think encompasses different types of solidarity. What characterizes traditional societies, where division of labor is less developed, where large families and dense communities dominate you would have more of the type of "friendly" solidarity you talk about. But in societies with high/greater degree of division of labor and differentiation, its usually the professionalization that creates a sense of mutual dependence between members of the community, each of which has different tasks. So in the sense, the traditional society we have solidarity where we depend on each other based on qualitative factors, but on modern societies, we depend on each other because of quantitative factors, like marked and economy.