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I've Googled several sources that compare two of these, but none that contrast all four:
Political Philosophy with Political Theory.Political Science with Political Philosophy.Political Theory and Political Thought. I haven't asked about the latter, as it looks to be a rarer term.As a bit of disclosure, I am a political scientist and have done work in political theory. By way of establishing my credentials, you can find my M.A. thesis online here. The claims below will be generally unsourced, because they are part of the professional knowledge of a political scientist.
This is actually the hardest to define. The most common definition is something like, "the things that we all have in common". The idea is that the actions of the government should be important to all of us, whereas the actions of private individuals and businesses are really not the public's business.
More practically, politics is whatever the government and politicians do. It involves how we choose leaders (elections, wars of succession, etc.), what leaders do (legislate, interpret laws, enact deals with other leaders), the formation of political units (nations, cities, parties), the activities of political actors (voters, juries, government officials, etc.)
Political science is simply a scientific discipline which investigates politics. The key here is 'science'. Political scientists are (typically) not interested in moral or ethical claims. Our goal is (typically) to advance our understanding of how politics works.
How does this happen? We formulate theories that attempt to explain how certain things work. These theories make testable predictions (called hypotheses). We test these hypotheses using a variety of methods including case studies, interviews, surveys, statistical analyses of data, etc. Based on these tests we refine our theories. Over time, we end up with a more robust understanding of the subject.
Somewhat confusingly, not all "political scientists" are "scientists". A major trend right now is work in critical theory, which comes to us from the humanities. Critical theorists do not offer testable hypotheses, but attempt to provide descriptive insights in a more philosophic way. Theory (including critical theory) is useful to scientists for helping us explore theories and generate novel hypotheses.
Political philosophy is any kind of philosophy which deals with politics. Examples include classics like Aristotel's "Politics", Hobbes' "Leviathan", and Adam Smith's "Wealth of Nations" as well as innumerable others.
Political philosophy is not a science; it does not offer testable hypotheses and it cannot be tested against the world. Like political science, political philosophy is a way of explaining the how the political world works (that is, both of them are a different approach to studying politics).
Many political science departments will have political philosophy specialists. This is partially for historical reasons, but also because their subject matters are very similar, even though their approaches are different.
Political theory encompasses two different things.
First, it is often a synonym for political philosophy. Easy enough.
Second, political theory can refer to the theories generated by scientific research. For example, one theory of voting behavior is the Michigan Model. If we talk about the theory without creating any testable hypotheses and evaluating them, we are engaging in political theory.
