Ni is paradigmatic and Ne is syntagmatic:
Ni thinks metaphorically like the paradigmatic axis above. Ne thinks linearly, like the syntagmatic axis.
If you look at the syntagmatic axis: "The man cried", you can see that the words "the" and "cried" are not related. They require the context of "man" to make sense. Furthermore, "the", "man" and "cried" make sense when you move along the chain from left to right, creating a specific idea, but if you were to move along the chain from right to left, your brain would have to turn it back around to understand it in the left-right pattern.
Meanwhile, the words in the paradimatic axis were always already related. I actually don't know how sang is related to died in this picture :=/ So you might need to forget about that for now. But the point is that the paradigmatic axis is filled with reference that are related to the word or idea by, say, rhyme, or reference - the paradmigmatic axis is basically just, "this information is stored near this information".
So the paradigmatic axis for "cried" might actually be "died", "coffin", "puffin" etc - Died is stored near coffin in our brain - the two words are related. Coffin and puffin are stored near each other in our brain because of the half-rhyme.
But if we were to say "died coffin puffin" it would sound like code. It doesn't make linear, cause and effect sense, like the syntagmatic axis does. So the Syntagmatic (Ne) creates new meaning. Ni does not create new meaning with the same type of direction, it projects using profiling. So it is aware constantly and unconsciously of related matters. It puts this together, in an unfollowable, non-linear way, by running through its files of related materials. When it comes up with the answer, what it has done is used experiential data in a creative way (by creating new patterns between materials or seeing metaphorical relations that are not immediately obvious) and from this data created a new picture from the convergence of a lot of previously stored info. So it has not transformed anything into something else. It has taken existing material and shoved it together to create a new thing. It can also project into the future by taking a load of references and, using prior knowledge of those references, calculate the probability of something happening. It predicts the future because it sees, automatically and unconsciously, probable paths that will span out from the circumstance it is in - it says - from what I know of the behaviour of this person and people who have shared similar traits is that they are likely to do so and so. It predicts that they will do this exact thing and it is usually right. I'm speaking from an INFJ perspective where Ni is working with Fe - but the Ni part is the profiling part. Think of the police. They say, the way this man has been killed points to a murderer who felt his/has this kind of lifestyle/knows this/is likely to be this colour/is likely to be this age - - - they profile from previous experience. This is EXACTLY what Ni does.
this means a few things:
1) Ni is STATIC, while Ne has DIRECTION.
I.e. Ni stands still and focuses on ONE idea at a time. It sees all related material and uses this to get a holistic and 360-degree view of the situation. It thinks VERICALLY - look again at the image. It is going nowhere, it is not creating new ideas, it is simply getting a total understanding of the situation with past, present, future, contextual data all being fed in and given equal importance.
Meanwhile, Ne grabs something and runs with it. It takes a situation and sees how it could be transformed into something else to create new meaning. It sees "The" and goes - the what? The man? What's he doing? Is he crying? Yes - the man cried - and they have taken "the" and made it mean something in a way that other people can understand. They are picking something up and using a cause and effect logic to move the situation forward into another situation, another context, another meaning.
2) Ni users don't know how they know, Ne users are more likely to.
Ni is an unconscious process. All those stores of information are locked up where the conscious mind can't see them. Ni users try to write a story and sit there thinking, I know what the character's like, I can't see a vague anamorphous shape and I can feel the tone of the piece - but I don't know what happens in the story. However, you also get a feeling that the story is IN THERE somewhere, hiding under the murk. And you'd be right. Your unconscious is working on it, creating patterns, projections, fitting things togeher, organisation the information. Then, when you're in the shower one day - POP! There it is, the whole story, laid out neatly for you. Thank you Ni!
Ne however, is a bubbling cauldron of ideas! It isn't struggling to draw ideas out of a murky mess, it has too many of them! And they're all so clear! Ne is prolific. Give Ne a pen and they can sit down and write a story start to finish, because they know what happens next - and that's how they work - this happens, then this, then this, then this. Ni is going: this is related to this, is related to this, is related to this - it's going nowhere! It's just understanding the situation not transforming it (yet!).
3) Ni is what you would call traditionally intuitive. Before we read MBTI stuff, we consider intuition to be an almost psychic sense. This is true of Ni but not Ne. Ne moves stuff around externally to create new things. Ni doesn't appear to do anything at all. It feels automatic - it's gut reactions, epithanies, sudden realisations - if you're in the US think of House, in the UK, think of Luther - one related subject spins off into a pattern of related subjects and puts the last piece in place and then SUDDENLY all is clear! And they can't tell you how they came to know - they just did, intuitively, all of a sudden. They don't know the process because the conscious mind never became involved.