What is the difference between behavioral science and cognitive science? Is cognitive science a part of behavioral science or vice versa?
The cognitive sciences are largely an element of the behavioral sciences.

The subject matter of the behavioral sciences is animal or human behavior. It is an interdisciplinary endeavor that involves a diverse set of fields such as psychology, ethology, behavioral genetics, criminology, etc.

The cognitive sciences study how the mind determines behavior via mental processes such as perception, reasoning, emotion, and volition. This also is a multidisciplinary endeavor involving neuroscience, psychology, artificial intelligence, and so on and so forth (see for example Harré, 2002). In the sense that the ultimate goal of (most) of the cognitive sciences is to explain behavior, they can be regarded as behavioral sciences. At the same time, it is clear that not all behavioral sciences focus on the mind as their explaining variable. Therefore it is the broader term.

It is important to note, however, that the cognitive sciences may investigate the mind without observing actual behavior in a given study. For example, there may be brain imaging studies without any behavioral measures. As another example, artificial intelligence research may simulate thought processes as a means to understand human reasoning, but conceptualize and measure behavior only in a very abstract sense. 

Sometimes, the term "behavioral science" is used more strictly to connote a focus on behavioral experimentation and observation. This usage would exclude some research within the realm of the cognitive sciences.

Finally, there is research that may be regarded as cognitive science that is not a behavioral science in any sense of the term. A case in point is artificial intelligence research that does not aim at simulating or understanding animal or human thinking.

References

Harré, R. (2002). Cognitive science: A philosophical introduction. London: SAGE.