This is a deep question. In his (February 1844). "Marx’s Critique of Hegel's Philosophy of Right." Translated by Joseph Omalley. Oxford University Press, 1970,Section 261) Karl Marx wrote that Civil Society and Families are related to the state. In fact, although they appear separate, dialectical movements between them give the impression that Civil Society and Family are identical with the State.
I am aware of another use of Welfare State used in the sense of a mixed economy defined by Paul Samuelson. He arged that problems like "stagflation is a basic feature of the humane welfare state that has repaced ruthless capitalism" (Samuelson, Collected Scientific Papers, Volume 5, p. 294, MIT press, 1986)
Japan was regarded as a 'welfare society' until the end of 1990s, because the state practically was not involved in the provision of welfare, but employers (corporations) and families.
More information is available here: https://books.google.com.ua/books/about/The_emergence_of_welfare_society_in_Japa.html?id=81m6AAAAIAAJ&redir_esc=y
Following the recent outcry on the living condition of the Internally Displaced Persons (IDP's) in the North-Eastern Nigeria due to insurgency, I made it known to people that the government of my country operates the residual model of welfare(temporary) ; where intervention is rendered through the national emergency management agency (NEMA) for the affected population to regain its lost structure or strength and be withdrawn. Other models include institutionalized and individual achievement , left for you to position your country. Above all, every society is a welfare society as its government provides for the welfare of its citizens in a number of ways ,whereas a welfare state is that which doesn't compromise its citizens hardships in nearly all situations. I refer you to the recent movement for universal basic income in Switz (audio documentary -Business Daily BBC World Service 11-06-2016).
In a historical sense I would be very uneasy about using the term at all, perhaps in the pre-modern welfare state.
early modern welfare "systems" in pre 1834 Britain until the foundation of the welfare state for instance national services c.1914. So prior to this there are generally three main areas which welfare historian such as myself are interested:
pre.1834 - old poor law and voluntary hospital period.
post 1834-1913 - New Poor Law period of mass regimented welfare relief, possibly the industrialising pre modern welfare system...
1914 - modern welfare state as we know. NHS, state pensions etc etc...
an abundance of literature on this issue in the past see: Steve King, Poverty and Welfare (2000) + Reinarz and Schwarz, Workhouse medicine (2013)
In the welfare state model public institutions are directly involved in management of health and social care, in the welfare society model, instead, the initiative in the health and social services is most of all of private (non profit) organizations.
It again depends I may be muddying the waters as a welfare historian, in the eighteenth-century welfare institutions were supported by what we call the "moral economy" or "religious philanthropy" discussed at much length in a book written by Donna Andrews "Philanthropy and Police", these non profit organisations were by the very definition welfare institutions, but were in actually set up to control the moral behaviour and activities of the poor...