Hi! I'll attempt to answer your questions in as few words as possible. Let's see how we do.
There are people saying that you can be a P but be very clean, organized and decisive, or J but messy sloppy pootchy pootchy
And that P/J isn't about that but about the function order
Idk but it seems like P/J is less big than lets say F/T and it completly changes the functions. Why? And if P/J is all about the functions and not about if you're decisive control freak crazy worker or a revolutionary hippie who doesnt like showers, how come thats what they say in the descriptions? Did P/J lost its very true meaning?
There are several reasons why P/J is the most important of the four dichotomies in terms of your functions but in order to explain why I shall have to explain to you how the four-letter indicator works to determine your primary functions. Take my type, INTP, as an example.
The first letter in a type indicator, "I", in my case, determines if your dominant function is introverted or extraverted. Your auxiliary function will take the opposite attitude. Mine is "I", so whatever my dominant function is, its attitude is introverted. So, at this point, I have four possibilities for my dominant function: Ti, Fi, Ni, and Si, and four possibilities for my auxiliary function, Te, Fe, Ne, and Se.
The second letter in a type indicator, "N", in my case, determines what your primary perceiving function is (N/S). It does not indicate whether the attitude of your perceiving function is introverted or extraverted, however. So, this rules out the S functions in my dominant/auxiliary, leaving me with Ti, Fi, and Ni for my dominant and Te, Fe, and Ne for my auxiliary.
The third letter in a type indicator, "T", in my case, determines what my primary judging function is (T/F). It is much like the second letter in that it does not determine the attitude of the function. This rules out the F functions, leaving my dominant possibilities at Ti and Ni and my aux at Te and Ne.
Now we get to the last letter. This one is a little complicated. The fourth letter in the type indicator, "P", in my case, indicates which function has an extraverted attitude, the judging function or the perceiving function. So, in my type, the perceiving function is extraverted. Because the first letter of my indicator dictates that my dominant function must be introverted, this means that my perceiving function is my auxiliary and my function order is: Ti, Ne, Si, Fe.
The reason why the P/J dichotomy presents the stereotypes you describe is because it determines which attitude we present to the outside world. The judging functions seek order and organization, so if you are a judging type you like to keep your external world as orderly as possible. Your perceiving function is not as concerned with organization and is more of a "free-spirited", open-ended process. So Perceiving types like to keep their external world open-ended and tend to be less externally organized, whereas their introverted judgement means that their internal selves tend to be highly organized and ordered. The same principle applies to judging types--their internal selves are much less ordered and more open-ended.
Now let's examine the effect the P/J dichotomy has on function order. Because that letter determines which function has an extraverted attitude, changing that letter will have some interesting effects. Let's take INTP again, and examine our introverted counterpart, the INTJ.
As I've determined earlier in this post, the INTP's function order is: Ti-Ne-Si-Fe. INTJs, however, have their judging function extraverted instead of their perceiving one. This means that it is their thinking function instead of their intuitive one that is the auxiliary and has an extraverted attitude, so their function order is Ni-Te-Fi-Se! As you can see, there are no functions in common with my type present in an INTJ. This is the main reason why, in terms of function theory, the P/J dichotomy is the most important one. If you change other individual letters in my type indicator, you will see that they still preserve at least one of my functions. ENTP: Ne-Ti-Fe-Si, ISTP: Ti-Se-Ni-Fe, INFP: Fi-Ne-Si-Te.
And S/N seems kinda the same. There are human beings saying that S can be very dreamy and use a lot of metaphors and be very interested in theories but still be like S. Its weird cuz typology websites seem to be in 3 clans: People who have some kind of N bias and everybody is N and S are dumb noobies who dont have any imagination, People who do what I wrote in the 2nd phrase, and people who don't understand anything(like me).
I'm not really sure what you're asking about with these two functions, however. And I just wrote a hell of a lot up there so I'm rather worn out. However, if you want me to explain anything I just wrote in more detail, don't hesitate to ask!