In light of looking at Beren's "philosophy of life" descriptions for the "operating Charter" thread; I find that they hold the key for completely cracking this confusion of Ni with Ne.
Ne: There are always other perspectives and new meanings to discover
Ni: There is always a future to realize and a significance to be revealed.
"Revealed" basically means "uncovered". So it's a matter of UNcovered versus DIScovered. They sound synonymous, but there really is a difference.
un- prefix of reversal (from PIE *anti "facing opposite, near, in front of, before")
dis- "do the opposite of" (from PIE *dis- "apart, asunder")
 
"uncover" or "reveal" implies that something was covered, and now we're reversing this.
For "discover", the object is not necessarily covered to begin with. It's just not known about, and instead of covering it, so it remains unknown, we're doing the opposite of covering it, and making people aware of it.
 
So "discover" reflects Ne's external focus, of meanings that are implicit in the object, yet are being made known to observers by the subject relaying the information.
"uncover/reveal" reflects Ni's internal focus, where a subject picks up a significance that has apparently been covered, and now reverses this by applying it to the various objects involved.
 
Also, we have meanings vs significance.
When I compare MBTI with the other temperament matrices, I first see that both include introversion and extroversion. So if they share that in common, I then wonder if MBTI has any counterpart to the other temperament factor of people/task. I eventually find that the factor corresponds to both T/F and J/P. So now, I "discover" this new (to everyone else) meaning of the T/F and J/P factors. The connection is already implicit in those external objects, but now instead of covering it up like it doesn't exist; I'm doing the opposite.
Ni is about significance, which is really a subjective thing, not directly implicit in the object.
A good way I have just thought of of describing this is what I have decided to call an "event template". Like I can remember being real young, and taken to the beach. It was an exciting new adventure; but IIRC falling into the water, and it was very scary and traumatizing. Later, going to a pool, I was pushed in. Going under water for me is very scary. So I had this sense of danger reagarding beaches and pools.
Years later, I catch the Brady Bunch episode where they go on vacation in Hawaii. I remember it was a very exciting event for them, and it seemed like it would be a great time. But then, these negative events start happening. I remember the hideous spider attack in the room. And the, the older brother wiped out in the surf, and was thought to be dead. There was this looming sense of a curse, from the Tiki they encountered.
Now this was not even my experience. It was fictional. Yet it tied to experiences I had, and formed what I'm calling a "template". A sort of situational counterpart to an archetype. I could name it like an archetype; such as "Hawaii-Bound" after the episode (though that title is not really descriptive enough). It also parallels Christ's statement "those who shall save their lives shall lose it", or "When they shall say 'peace and safety', then shall come sudden destruction". Again, when we think things are so well, all horror breaks loose. So I could call it "peace and safety".
This would form a mental background future events would be engaged against. They then take on a significance. Like I cut my finger really bad on a family outing to a beachside resort, on a 104° day in a hotel with no A/C, but the windows painted shut from whern there were A/C's. This seemed to fall right into this template, though I probably wasn't even thinking directly about the Brady Bunch episode. It was just this background sense of things being "too good" on the way to the outing, and thus something go horribly wrong.
Another template is based on Aliens, where they make the exicting discovery of life on another planet, but the guy has the horrible experience with the face-hugger. When it comes off; it seems he is all right, and he tries to move on from that trauma and in somewhat of a daze, get back to normal life by eating with the others. But then, that's when the horror of horrors happens. The alien inside him bursts out. This is what loomed in my mind as I had to walk around in this heat after loosing so much blood, and I tried to be OK and get back to normal, but the others were saying I was not completely myself, and almost in a daze. Luckily, no further horror happened after that. Still, it all fit into these templates.
The templates are purely my own in applying to situations; hence, introverted, and yet they do tie into universals (hence, other people using the same concepts), which is also characteristic of introverted functions. Those would be the internal "focal points" of the illustration I posted.
So what ends up happening, is that whenever there is some really exciting event or prospect, I have this fear that something really bad is going to happen. Of course, Ni for me is in the shadow, in the "Senex" or "critical parent" position. It is negative, and very incomplete, and not a good guide at all.
So now we see the basis of Beren's description of Critical Ni as "putting a damper on plans for the future with negative thoughts of how things will be". It's based on a sort of negative template. My "good" parent Ne tells me that the negative is only a possibility, but more likely (looking at the external data available so far), things will go all right. Yet for some reason I lock on to this negative possibility. I'm no longer exploring possibilities; now I'm inferring significance. (For the record, since this deals with stressful events, it can likely be seen as a manifestation of the archetype. I otherwise don't usually trust or think much of such a process).
For NJ's, this function will be more mature, and they will have more positive uses of it, which will also be more likely to come true, as more indepth, complete templates will be created, which will pick up more cues on whether a particular outing really fits into the template that ends in disaster.
Ni is often described as dealing with "frameworks", which is a term usually associated with Ti (also making it confusing). But Ti deals with frameworks of judgment, you make decisions with, such as sets of principles. Ni would deal with frameworks of perception, in which you take in new information. I would say all four introverted functions have frameworks. Ti is logical frameworks (involving 'principles"), Fi is ethical frameworks ("values"), Si is concrete frameworks (i.e. memories of how things should be), and Ni is abstract frameworks, such as these event templates.
 
Ni is often confused with Si even, because a person can look at how events play out over and over, and then get a sense of what will happen in the future. However, this can be Si. Looking at how gravity always pulls things down, and then deducing that something you let go of will drop would be Si. It is concrete data. It's the act of creating a template of events that is the process of abstracting (from memories), not just any "foretelling" of the future. It generates a concept.
The whole "Bad things will happen on a fun outing" is not based on concrete facts such as gravity. It is a model pairing together otherwise unrelated events that only share a few details in common, such as going to a fun outing. There is no external element connecting the two to any common negative chain of events. It's all in an internal template, or perhaps 'storyline', if you will. Another example is conspiracy theories. In this case, the negative outcome has already occurred, and now you employ a template of conspiracy scheming to "reconstruct" how it was carried out. (The "blaming" aspect of this will be especially pronounced for those of us with this process as the blaming "critical parent"!)
 
So just as you can experience a current event, which is Se, or abstract a new meaning from it, which would be Ne; you can also look back at a memory, which is Si, or abstract significance from it in the form of things such as these templates, which would be Ni.
This also brings to light the fact that the simplistic descriptions of Ni as "foretelling the future" really do not do the function justice. This is what has made it so hard to figure out all this time. And any person who seems to have some sort of "visions" of the future is automatically made into an NJ type. The templates may give you a sense of what will happen, and you can loosely call them "visions", but they are not glimses into the future.
Another example is in one of Berens' descriptions of Ni; a person choosing a dog has a "vision" of a dog barking and crying, and then realizes that they should get a dog that didn't mind being alone. This doesn't even have anything to do with any particular singular event being "predicted". It was a template or model of a situation that was referenced to inform a decision for the better, to avoid that template possibly being realized in a future event.
This makes it more clear to me, about a close friend of ours, who I always typed as ISTJ because of being pure "Melancholy" on the APS. Yet there was this problem (for my correlation) of her having these "visions" of things. And other people in the churches (which are charismatic-leaning) who otherwise seem SJ, say they have these "insights" as well. Yet I have realized that these visions are totally concrete in content. Like seeing a dome shape, and then, an event occurs involving a dome. But this is not Ni. Ni is abstract. Now, if the dome was a symbol of something, then it might be fitting into an Ni template. Even though the aforementioned dog vision seemed concrete, its application was clearly an abstract model, and again, not a hard prediction. They claim the insights are gifts from God, and that would be more fitting than a natural cognitive preference. The cognitive process test I am seeing confuses both Ni and Fi with such oversimplified descriptions in the questions, and SFJ's end up coming out as ISFP's (yet with very high Fe!). Yet I find; you give some of them some real Ni, they tend to think it's crazy, as fitting for something deep in their shadow.