The primary difference is two-fold:
1) Methods : Social sciences use mostly qualitative methods and content analysis, psychology and cognitive sciences use quantitative methods and statistical analysis. The one basic standard tool in psychology and cognitive sciences is the laboratory experiment, while social sciences usually collect data in the field.
2) Object of study : Social sciences deal mostly with social entities. The smallest social entity is two people. Psychology and cognitive sciences deal with individuals or, if they deal with populations, the general characteristics of the individuals of that population. Psychology and cognitive sciences deal with social processes only from the perspective of the individual: how individual internal mental processes are affected by them.
As usual, this is a tendency, and the borders between the disciplines are blurred. There is no clear distinction and there is a huge overlap where research could fall in either discipline and is associated with one only because the researcher comes from it. Also, in academic institutions, certain parts of one discipline might have found their home in a neighboring discipline for historical reasons, e.g. pedagogical psychology is often placed in the faculty for pedagogy (a social science), but there it is just as often taught by psychologists.
I wrote "psychology and cognitive sciences", because cognitive sciences is strongly associated with psychology, but also with information sciences / computer science and neurosciences. At our university, the degree program "cognitive science" is part of both the psychological and the computer sciences department. But other universities place it elsewhere. Like neurosciences, cognitive sciences is an interdisciplinary field or, if you want, a new and evolving discipline whose realm is even less clearly defined than that of older and more traditional disciplines. Nevertheless, I understand cognitive sciences to be concerned with cognition, which is an aspect of the individual, and a traditional field of study that lies mostly within psychology and other natural sciences like medicine and biology.
In short: cognitive sciences is a natural science, while social sciences are part of the humanities, with all the methodological and theoretical implications that follow from that.