The main difference between the two is their way of dealing with the topics they have studied and their methodologies.

Political philosophy is concerned with what it should be, pursuing the ideal. Political theory tries to define and explain. For example, political philosophy asks "how is the best state?" In contrast, political theory tries to answer the question "what is the state". It tries to reveal this answer from a concrete situation.

In my experience, the terms political thought, political theory, and political philosophy are frequently used interchangeably. However, when used differently, I see political thought as unsystematicallyy capable of including poetry in addition to elements of the more clearly rationally testable ideas expressed by the prose offered both by political theorists and political philosophers. In contrast to political philosophers, political theorists may only seek to identify clearer ways of dispassionately describing the political institutions, activities, behavior, and events in the world – ideas that can be tested against empirical evidence and logic. These theorists see their studies as a branch of ‘value-free’ political science – the disciplined attempt to determine the facts about past and present empirical realities – descriptions and probabilistic theories about how politics works. They do not attempt to prescribe or suggest how political realities might be improved. In contrast, I see political philosophy as the attempt rationally to workout how existing political realities might be optimally improved, how justice might be secured, both because and inspire of the facts as determined by political science. Political philosophy tests its tentative conclusions additionally by continuing its dialogues with all the other branches of philosophy which are focused primarily on the other sides of human life and all the non-human realities.

I like Fatih's answer which comes close to a definition of political philosophy once given by Leo Strauss (see: ' What is Political Philosophy') as defining a branch of philosophical inquiry that attempts to examine politics in relation to broader normative or epistemic endeavours; for example, the realisation of the 'good life', or the pursuit of universal knowledge and understanding; whereas, political theory in contrast may seek to reverse this question and ask something instead to the tune of "to what extent is the 'good life' possible within the logic of political organisation, or to what extent are different political subjects capable of actually understanding one another?"

Adam Taylor made a good point. In this respect, if we consider politics without its normative and epistemic basis, we will limit our vision of "good life" to "what is".

I'm not sure that the distinction is always as dichotomous as labeling political philosophy as normative and political theory as empirical. In my experience, I have heard of normative political theories as well as political philosophies that are more empirical. I have also heard the same texts be referred to using both terms. Perhaps this is due to terms being used incorrectly, or perhaps it is an issue of increasing compartmentalization among subjects of study and less communication between philosophy and political science.

Another way of looking at this would be to consider if one of the terms would be encompassed by the other, or in other words, if political theory in itself is a political philosophy or vice versa. After all, is a theory's goal not to provide an ideal explanation for a phenomenon? Conversely, is political philosophy's goal not to provide an explanation for what is an ideal iteration of a phenomenon, thus attempting to describe what something is even if that something does not currently exist? If political metaphysics exists or were to exist as a subject of study, would it be political philosophy or political theory?

Furthermore, could a work contain both political philosophy and political theory? Even if the political philosophy=normative and political theory=empirical dichotomy is accepted, would a normative work of what the ideal is for a particular thing not need to be based on some kind of empirical understanding of how the thing works? Does political philosophy require some kind of political theory to first exist or vice versa?

For both, the methods used also vary widely. The subject of metatheory, involving discussions on how to write theory, may provide some insights on best practices for political theory, and it may have elements that are beneficial to political philosophy as well. Here is a source that may be helpful:

Neufeld, M. (1994). Who’s Afraid of Meta-Theory? Millennium, 23(2), 387–393. https://doi.org/10.1177/03058298940230020401

A conceptual history point of view might help us shed some further light. To my readings, 'political philosophy' is a rather late 18th and mostly 19th century term that gains its most firm academic standing in the original making of 'political science' study programs around the world and consisted in the effort to teaches the acknowledged 'philosophers' and 'philosophies' by that time as meaningful or useful knowledge for 'political science' students, whereas 'political theory' finds a place in such programs only well into the 20th century. This being so, it might be more suitable to place under the label of 'political philosophy' approaches to knowledge appertaining to politics that display an interest to consider themselves in the light of available philosophical interpretations or that work in quite close terms, such as Marx and the Marxists once upon a time, Leo Strauss, John Rawls etc. Even though such approaches are quite prone to display an interest in what are nowadays called 'normativity' or 'deontology', this is not necessarily so, since several political philosophies have proven more than welcome to concrete observation and empirical studies, favouring also attempts to apply ideas in situated practice, such as Montesquieu, Bentham, Tocqueville or Mill. 'Political theory' seems to gain ground once 'political philosophies' are canonized enough for many scholars and academics to be interested to reason or reflect on more concrete political issues without necessarily passing through all this educative and interpretative process. In these respects, it remains legitimate to view all 'political philosophies' as having been successful 'political theories' back in their formative times, whereas the most telling 'political theories' will probably have more than few points of connection with 'political philosophies'. However, we are losing many things from the picture in case we do not hold such minute distinctions in mind. Nowadays, with the explosion of academic education and the craze with being highly subjective in the humanities, 'political theory' is gaining very strong ground, to the extent of it being often used as a replacing synonym for 'political science' or as calling for doing away with 'political philosophy' if not 'philosophy' as a whole. However, we would once again lose too many things from the picture in case we did so. Don't you think?

The difference is that political theory is the name given to a sub-field within political science departments, whereas political philosophy is the name given to a subfield within philosophy departments. In terms of actual contents you can find the same thing, or entirely different ones, labelled more or less indifferently as political theory or political philosophy. It is also a peculiarly anglophone distinction, due to the history of how the academic discipline of political science defined itself (mainly in the United States), that does not exist in the same way in non-English-speaking countries.

Do non-English speaking countries pick either political philosophy or political theory as an overarching term or is there another term used to refer to both?

In the context of this question I must quote the words of Bernard Crick, "Political Theory attempts to explain the attitudes and actions arising from ordinary political life--thus political theory is basically concerned with the relationships between concepts and circumstances." On the other hand "Political Philosophy attempts to resolve or to understand conflicts between political theories which might appear equally acceptable in given circumstances....."

Guido in his first sentence gave us a very clear definition of both concepts. Thanks.