This is usually how it works. The local and federal government earmarks a certain sum of money each year for specific sorts of charity. The federal government then dumps a lot of that earmarked money into state coffers, based on current requests and previous levels of need. The way this money is distributed is heavily regulated. The downward flow of money is often necessary because of various laws protecting states rights and also in recognition that the locality in question has a better understanding of local needs than the federal government.
The state then uses some of those funds to provide aid to citizens, but largely this money, in addition to money from state and county taxes, goes to private charities via grants, bonds and the like. Heavy regulations (now at both the State and federal level, and sometimes the county and city level as well) attend these funds and aim to ensure that the funds provided are used for the intended purposes.
The reason it works this way is that it (a) helps the same people it would have helped, supposedly, if the aid had been granted from a federal level or from the state, (b) creates local business opportunities for these private charities,and (c) has more streamlined, efficient organizations addressing the citizens’ needs rather than a state or federal bureaucracy.
Most major private charities function with hefty state and/or federal subsidies, whether they be local grants, federal or local bonds or funds from both sources (tax credits, for example, are provided by the federal government, and awarded by the local). DC, for example, awards a little over $8M in contracts to the Archdiocese. The Archdiocese spends a little of $10M of its own money on charity work. The reason for the collaborative charity works is many fold including, but not limited to, reasons of economy of scale (DC can only earmark x amount to spend on a social need, which could really use 2x amount of dollars… having Catholic Charities take a grant of x to handle this is an easy way of achieving your goal), reasons of law (grants sometimes come with special exemptions normally only afforded to government programs, which exemptions allow the charity organizations to effectively administer aid in a manner otherwise prohibited), and reasons of efficiency (it makes more sense to have one person overseeing a certain charitable effort than two or many).