What is the difference between political science and politics?

Political Science, as one other answer notes, is an
academic discipline. However, it is far broader than simply the study of politics.
Political Science does involve the study of politics, but it encompasses also the study
of political systems around the world, including the structure and functioning of
disparate governments in every region of the world. Governing structures vary widely
around the world, especially during the Cold War, when the Soviet Union and its
satellites and allies in Eastern Europe and across the so-called "Third World" were
governed by brutal totalitarian regimes that often had forms of parliaments that were
simply "rubber stamp" institutions that provided a thin veneer of respectability for the
dictators who actually ran those countries. In other words, communist regimes had
"central committees" and other ostensibly legislative bodies that, in practice, merely
affirmed decisions made by the top handful of members of those governments' ruling
circles, usually known as a "Politburo," or Political
Bureau. 

Within the narrow definition of "Political
Science" provided in the other answer, the field does, as noted, involve the study of
politics, such as the factors that cause people to vote a certain way in elections,
public confidence in the governing structures, and divisions within electorates that
help to understand the perceptions of different ethnic groups or socioeconomic classes
toward various issues and politicians.

"Politics" refers to
the practices of elective and nonelective political systems with regard to the manners
in which leaders are elected or appointed, the minutiae involved in political
campaigning in democratic systems, the dynamics between and within disparate factions
within any particular system (for example, relations between so-called "hard-liners" and
"liberals" or "moderates"), and the relationship of citizenry to governments. In a
democratic system, politicians (those seeking elective office such as mayor or
congressman) interact with the public whose votes they need to win an election. In a
nondemocratic system, the focus is more on relationships within the governing party or
regime. All of this constitutes "politics." Political Science is the study of all of
this, as well as of the economic systems of different countries and the manner in which
relationships with other countries or political entities are
conducted.