Even though I don't consider myself a full 'natural' yet (like the more advanced guys here), I'll give my two cents....
besides what The Kidd and others have already said, one thing that I have seen that naturals have in common is that they don't look at women as goddess or as something that you need to worship. In other words: they were not affected so much by social conditioning.
for me it was and still is a journey. Because of social conditioning from the media and the environment I grew up in - I used to look at women as something to worship...
then, when I read The Kidd's articles things started to change. I also saw David X's seminars and that also helped. After reading 'the manipulated man' and 'the great female con' things have became even more clear. And now: when I come back to The Kidd's articles I'm able to understand them better
So I'll give an example on one of the natural's mindset:
Since they don't think that there is anything special about women they can approach and talk to many women (let's say 200 women) for the purpose of getting sexual with them.
even if 199 women reject them and then 1 accepts and has sex with them- they will say:
cool (Paul Janka is an example of this...)
The PUAs on the other hand, approach all the time but since they still beleive women are so special, every rejection they get - they carry it around with them in the back of their mind. And it hurts their self esteem...
(This is a very importent piece of the equation)
Even Zan who calls himself a natural and teaches guys to worship women- if you read some of his old posts at the fast seduction archive (before he had his natural game Bizz), you will see that he doesn't give a shit about women or in other words: he doesn't think that they are something special or something that needs to be worshiped.