Smaller agencies are generally contracted out to do basic social services such as child abuse prevention, foster care prevention, family preservation, foster care services, etc. Generally speaking, the quality is better since the agencies aren't as "overloaded" as the county and the costs are generally kept down because case planners are not paid as much as the traditional case workers, however, it's usually county funds that pay for this.
Other social services such as housing assistance (including emergency housing services and fema fund distribution) are also done on a smaller basis in a community organization. This is done by private funds, city & federal funds but doesn't seem as common with DSS funds.
Educational services can come from a variety of sources such as Buffalo Public Schools (for the SES programs driven by "No Child Left Behind"), Department of Labor (for career and vocational exploration programs), City of Buffalo (Mayor's Summer Youth) and private sources for basic tutoring and remedial services as well as Scholarship programs and distribution.
There are alot of areas of duplication, however, each agency generally has it's own population it serves (usually because of physical location.) Also, what is considered "housing" assitance to one agency may have a different definition to another.
Some agencies are bound by physical lines (such as streets that border a certain section of the city) as to whom they are "allowed" to serve while others can cover all towns and cities within a county or multi-counties.
Other social services programs are funded from mother agencies such as the United Way. They have their own terms as to how they're organized and who gets the grants.
Basically, it all depends on the funding sources and what the contractual terms are and what the agency specializes in.