What is the difference between political ...

Political philosophy is the study of fundamental questions about the state, government, politics, liberty, justice, property, rights and a persons relationship to society.

Political theory deals with existing states of affairs, and insofar as it is possible to be amoral in its descriptions, it seeks a positive analysis of social affairs – for example, constitutional issues, voting behavior, the balance of power and the effect of judicial review.

Simply put philosophy is the discipline concerned with questions of how one should live.

Theory is a logical explanation or testable interaction that can be proven to be true or false through a study of the facts.

I think "tiptopmanager" has a good answer, but I would add that political philosophy is likely to be abstract, idealised and making assumptions about how people "would" behave under conditions that are always within the boundaries of the parameters the philosopher has given them.  I loved the idea of Plato's republic when I was a teenager.  It seemed like society would be wonderful if we only had not overlooked such a wonderful plan of how to organize human beings into a well meshed and harmonious whole.  The problem is that it was not a practical guide to the care and feeding of large populations of largely irrationally self-centered and self-serving creatures that men have become (long before Socrates time, mind you, and little changed today).

Political theory, in contrast, is likely to be concerned with the specifications of the cages and diets of those beasts we call populations, and whatever practical methods one can devise to predict, control, or at least prevent them from destroying themselves and the planet they live on. 

Hermann Goering, the Nazi politcal minister and leader had a very good grasp of how this worked.  There is a famous quote attributed to him (I believe the claim is that he told it to a "keeper" of his after he was sentence to life in prison) that tells how leaders manipulate "the people" using accusations of lack of patriotism, and fear mongering, in order to lead them into wars that "nobody" wanted (except the leaders).

I found the quote while I was checking the spelling for Goring.  Here it is.

Naturally the common people don't want war; neither in Russia, nor in England, nor in America, nor in Germany. That is understood. But after all, it is the leaders of the country who determine policy, and it is always a simple matter to drag the people along, whether it is a democracy, or a fascist dictatorship, or a parliament, or a communist dictatorship. ...Voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is to tell them they are being attacked, and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same in any country.

Now THAT is a political THEORY, almost as predictable as the "theory" of gravity.

Sincerely,

Stafford "Doc" Williamson

Political philosophy is abstract thinking about concepts such as justice, liberty, equality etc. While not necessarily divorced from facts, it's conclusions are supposed to be valid without reference to specific facts. For example, the statement that freedom should not lead to limits on the freedom of others can be supported by political thinking without the support of facts. Political philosophy is essentially moral philosophy applied to political structures. It studies morality in the setting of certain political systems.

Political theory may engage in similar studies, but will also claim to be scientific in the sense that it constructs theories which should be verified or falsified by empirical studies (for example quantitative analysis) executed by political scientists, sociologists, psychologists etc. 

     Political Theoiry is akin to Political Philosophy. Philosophy is the pondering of matters and applying both logic and Ethics to those thoughts. Philosophers are usually sought out by those who want to learn the propriety of an action or theory, not simply say "it sounds good, let's do it!" Theorists on the other hand are more prone to simply writing about a subject and have little interest in the ethics of their theory, advancing it simply as 'what I believe' and not caring about its propriety or practicality. He will support efforts to overthrow a government simply to see his theory brought to action.
     As with any theory, it can never be fully proven and will always have flaws and impurity in it. Philosophers however will tackle the propriety/practicality performing small experiments here and there. If deemed fit or conscionable, then it will be suggested. Philosophers tend to believe that all within the realm of a governance should vote yea or nay on the proposition before applying it, and tend to lean toward republics or democracy rather than aristocracy theocracy or dictatorships as a better ruling power.

Greed.