Well, I was recently a social work major, so I can try and help, but I may not be 100% accurate.
Social Services, in these scenarios, kind of work as a channel between the family and the services that would provide this women with care. Because the women's identity is unknown, it is more likely a police thing, but the Social Worker would work with the women, trying to keep her comfortable and be there for later on, after the family is identified. Once the family is found, the social worker would introduce the family to options, such as keeping the woman in a home or list resources if the family wishes to go with home care. They would also show them counseling resources, to help the woman and the family cope with the new scenario.
I'm not sure about the location, whether they would check her in to a temporary care residence, like a nursing home or hospital, but either would have access to clinical social workers.
Social Work tends to branch off in two directions: General and Clinical. Clinical is more on the medical side, dealing with illnesses such as dementia or counseling for individuals families that are losing a loved one from cancer or other illnesses, or are trying to connect people to resources like hospice care.
However, certain organizations do have social workers in both areas, ones that attend to the more medical setting and those that work with children and families. Generally though, they wouldn't overlap in there responsibilities, unless the children and family are connected to the illness and are working with the social worker for that reason. If it is a matter of abuse or even just a child acting out in school or in low income situations, then more likely than not, they would be dealing with a Child & Family social worker.
The training for the two areas are widely different, Clinical Social workers learn a lot more about the medical side of things and are familiar with the terminology. Also, in order to become a clinical social worker, you HAVE to have a master's degree (9 times out of ten) in that profession (or other medical related areas) and also many times, a PHD, while in other areas of Social work, there are countless of degrees you can have--some with little or none training on being a Social Worker, like English or History.
So, in all, Social Workers can work in many environments and generally have diverse cases and experience depending on their current organization , but clinical and other general social workers don't blend cases often, unless the situation that they are dealing with is for both. Though, even in those circumstances, Social Work is a team effort and many social workers will talk and work with each other in order to provide support and give effective care and help to their clients, so there can be multiple social workers who help out on one case.
Hope that some of this helps!!