I'm not that messy. My mess is more of a "controlled" mess where if you did a quick glance over the room it will look slightly neat, but if you look closer you'll see dirty clothes in the desk chair and papers stuffed under the bed.
Anyway, I don't see being disorganized as something to aspire to. If I had the choice, I'd be neat; not excessively so, but enough. Just because I like aesthetically pleasing surroundings. But when I try to be, it doesn't work out.
I don't think it's anything wrong with saying you're an organized and tidy person. Like for example, one of my friends asks me to take of my shoes in her apartment. I don't think that's anal or OCD. It's her place, she doesn't want her carpet to get dirty and I respect that. If someone wants the space around them to be reasonably clean then I'm not going to all salty about it. I often find these threads go in the direction of NJs saying how un-J they are because real "Jness" (whatever that means) is what SJs do.
How my J manifests itself is more conscientious and closure-orientation than anything else. If I use a sink and splash water everywhere I take a paper towel and clean it up. If I'm in the grocery story and someone is buying one thing and I've got a grocery cart full of items, I let them go in front of me. I put things back the way I found them. I don't lose people's stuff they loan me and I return it in a timely manner. I keep my personal business documents organized and in a file cabinet. I'm not particularly good at keeping up with things like car maintenance, but I'm very people organized. I also make decisions fairly quickly and know what I like and want without a lot of cogitation.
The most stereotypically J people I know are two INTJs and INFJ. The INFJ makes lists on her cell phone, makes me take off my shoes when I enter her apartment, has all her shoes organized in clear plastic boxes, and asks me to pick up a crumb from a potato chip if it drops in her office. The INTJ, well, he's just horrible. I've been chastised for not keep my windshield clean. The other INTJ gets quite testy when we don't RSVP to events she organizes or return texts within a "timely manner." And these people aren't particularly light INJs either.
To the OP, yes there are some people that give off a stronger J and P vibe than others. My ENFP division director is very P-ish in her mannerisms: breezy and moves quickly from one thing to another, very "we'll work out that later" with nothing really finalized. My INFP director is more organized, but I feel like it's more of a learned trait (she's in her 60s) than a natural tendency. Her general feeling is still more P-ish in that I can tell in her personal life she's more go with the flow than professionally.
The vibe of my two ESFJ and ISTJ coworkers is not necessarily that they're obviously physically organized, but they are more closure-focused in their speech and actions. They take definite moves to move something along towards a goal, i.e. "Let's have a meeting to discuss this" or "I'll email this person to see if they're interested." Not that other types don't say this, but it's a more consistent moving a process towards something and giving/seeking direction. Compare to my NFP directors who will mention something in the hallway and that's the "meeting" or make remarks more casually with information dissemination being less official or linear.