I see a couple of different parameters that define J and P that aren't necessarily related.
Certitude in ideas - Thinking in terms of conclusions
Closure oriented - More comfort with decisions being finalized
Initiating/Acting onto the world (this might be extroversion EJ in particular)
Uncertainty - Thinking in terms of possibilities
Open-ended - More comfortable with options
Responding/Reacting to the world (this might be introversion IP in particular)
I bolded the parts I identify with and see a distinct relationship between them. I've mentioned this before, but I am rather organized because it is the way I remain open to new ideas or even new belonging that go in the closet. The structure is an open-ended system that allows for new acquisitions easily. One can metaphorically throw new stuff into a messy closet (and perhaps know where everything is), but that doesn't allow it to have its most meaningful relationship to what is already there or make it as clear what needs to go. Structure can increase fluidity.
I have had an employer that is my exact opposite, who confuses me on this J-P issue for the same reasons I confuse myself. On the one hand she has the most intense certitude and is forceful in implementing her plans and ideas. Her presence is absolute, intense, no debate, just finality. She would be the extreme J by many estimates. However, she is also intensely random and works best in a highly controlling, yet potentially unstructured scenario. Plans can change quickly. She is comfortable acting on impulse and has stated this. It is a kind of certainty-random pairing that seems extremely J and P at the same time. It separates the exact same two poles I notice in myself, but exists at the opposite end of both.
My point is that on the one hand I find the distinction confusing. The most prominent stereotype of J vs. P is to transplant the Type A and Type B personality assumptions onto it, but neither accounts for everything.