Is the following true?: "All political scientists are not politicians and not all politicians are political scientists."
This statment is true, because in fact most politicians are not political scientists. Political science is an academic discipline devoted to the study of politics. Political scientists study such things as comparative political systems, voting patterns, polling data, and political rhetoric in order to understand how politics actually works. Politicians, on the other hand, actually do the work of politics, campaigning and running for office, and actually developing and implementing policy. In order to do this, it is not necessary to have an academic background in political science. In fact, many, if not most, politicians do not have formal training in the field. And most political scientists are not likely to run for office during their careers.
This said, however, modern political campaigns employ dozens of specialists who analyze polling data, craft messages and positions for their potential impact, and other aspects of politics. Clearly, many of these consultants and staffers would need a strong background in political science, and many are actually academic political scientists. So political scientists are important to politics, even though the statement referenced in the question is correct.