Political philosophy is a subfield of philosophy. Political theory is a cognate subfield in political science. I frequently referee papers in both subfields.
In some cases, the difference between the two is minimal. (For instance, the Princeton theorists read like philosophers.) But in many cases they are quite different.
Generally speaking, one of the major differences between the two has to do with clarity of exposition. Philosophers usually state their thesis up front, clearly state the premises and reasons supporting that thesis, and try to go out of their way to be clear. Theorists often don't; indeed, they seem to aim to be unclear. You can get 20 pages into a 30-page theory paper and not yet know what the paper is trying to do.
In particular, theorists often make a move I like to call "the argument in the pocket". What I mean by this is that instead of stating their argument, they sort of hint or gesture toward the idea that they have an argument hidden in their jacket pockets, but haven't quite shown it to you. They'll say things that are the equivalent of, "You know, like Arendt said," and then you, the reader or listener, are supposed to fill in the blanks. This sort of move creates the appearance of depth and erudition, and thrusts the responsibility for making the argument onto the reader or listener. It insulates the theorist from criticism, because the theorist maintains plausible deniability for any objection the listener/reader might make ("Oh, I didn't mean that"), and further, it insulates them all while trying to make it seem like the reader is the dumb one ("Oh, you don't know what I mean? I guess you don't read Arendt enough.") We're supposed to guess what the hidden argument is, and if we can't guess it, it's our fault.
Anecdotally, I can't think of a single time where, once the hidden argument in the pocket is revealed, it turned out to be any good. This move is almost always made because the theorist is confused or lacks a good argument. They're hoping the ambiguity will bully the reader into compliance.
In philosophy, the norm is, "I don't know what you're talking about, so you need to do better." In theory, we often see instead, "I don't know what you're talking about, but you say it in a fancy way, so I should probably presume you are saying something smart."
Another way of putting it: Somebody has to do the work of making the argument and writing the paper. In political philosophy, the norm is that the author does the work. In political theory, it appears to be common (say, 1/3rd of the time) that the reader is supposed to do about half the work of constructing the paper.