It seems that being killed by another player for no discernible reason can be the most infuriating occurrence in the game. The delineation between the two groups probably evolved naturally due to Player Killing eliciting such a strong reaction from those who have "suffered" it.
When unfriendly NPC's or other critters attack you on sight it's easy to shrug it off, they have no choice in the matter. It's how the game was coded. However when another player attacks you, it's apparent that it was a conscious decision made by the person controlling their character. Some players can shrug it off, others can't. It feels personal to them, for understandable reasons. I wouldn't be upset at a tree limb if it fell on my head, but I would be fucking pissed if my wife hit me in the face with a baseball bat without provocation. There is obviously transference from real life into the game for some players.
I think where the mindset really differs between PK and APK is how the act is viewed. Raiders, Highwaymen, Floaters, and other critters are simply game obstacles to present the player with a challenge to overcome in an encounter. I tend to view PK's (myself included) as an extension of that role, whereas those of the APK mindset obviously don't see it that way. I've had discussions with adamantly APK players who have told me that they feel PK's are terrible people in real life as well, and their play style is only a reflection of that.
I don't feel that either group is wrong, it's just a different point of view. At the end of the day, it gives each of us purpose and drives gameplay forward.
I know I've painted with a fairly broad brush there, but I do understand that each player is different. We all have different motivations and ideas about the game, and no two players are the same. Some are very extreme one way or the other, while some are more middle of the road. In these conversations, it is usually those on the extreme ends of the spectrum that are made example of, so it's the easiest context to discuss it in. I'm not attempting to pigeonhole people firmly into anything.
That being said, I really can only speak for myself with any real validity. The above is all opinion based on observation, and in many cases is totally inaccurate.