I'm seriously not trying to be difficult, and I'm sure there's just something I'm missing here, but that doesn't sound any different than the way I used to write papers and study for tests (when I was in school). But, I don't have any kind of magical thinking - just the normal ability to draw connections between concepts and to spot patterns.
I apologize in advance for this long post, but I'm really trying to understand this, and wanted to explain where I'm coming from, and what my stumbling block is.
I'll try to describe how I think Si is often confused with Ne or Ni. Si is often pejoratively described as being judgmental, and even inclined to bigotry. While I definitely take exception to the bigoted label, I do think it's true that Si develops stereotypes, and stereotypes - when used by a small-minded person - can form false rationales for bigotry.
Stereotyping isn't all bad though - it's used in very smart ways by advertisers, politicians, lawyers, sociologists, etc... It's being able to instantly know (or have a pretty good idea) of which people are likely to buy a certain product, vote for a certain candidate, or which juror will vote to acquit. That requires quick associations that anyone can make: country singers probably shouldn't advertise in Vegan restaurants, or (for common political wisdom,) Subarus are for Democrats. These things are done by all people, all the time, but are probably especially common to people who use Si, because as a function it seeks to categorize the environment.
But in other contexts, that same functional ability is mistaken for Ne (because it usually accurately predicts a pattern based on unrelated information, and it picks up on coming trends very easily) or even Ni (because when someone is really good at it, it can seem like mindreading).
I've heard a lot of people suggest that in Si-doms, those associations are based on building-block connections, as though there's a conscious chain of data that leads from one fact to another. If those connections exist, they certainly aren't conscious. I've also heard people suggest that it's based on personal experience. Maybe, but it constructs a grid that goes far beyond those experiences.
I've been able to draw the distinction between the use of Si and Ne by drawing the line at reality and imagination. The Si function is extremely good at predicting, but less good at creating. To put it another way, I'd probably be pretty good at playing the stock market (if I, you know, had both the desire and the money), but I'd be pretty bad at designing a new product from scratch. Second, the connections made by Si-doms are all between real-world factors: comparing one historical era in one nation to a different era in a different nation; describing a geopolitical alliance using a high school as a metaphor, etc... My sense is that the associations made by a Ne-dom would be impossible to explain - like comparing a farm animal to a musical note. That's a rare gift and would account for Ns making up only a few percent of the population.
Back to the Stewart example. Yes, he makes connections quickly and uses those connections to toy with his guests. But those connections are reality based and functionally no different than the way I interpret and use information. Compare that to Colbert who plays around in the realm of the fantastical (changing facts on wikipedia, creating his own comic book character...) To me, that's a pretty good distinction between a highly intelligent and talented Sensor and a highly intelligent and talented Intuit.
This is why I get confused when Ne is described as proficiency in comprehending concepts/theories or making associations between disciplines (both of which seem perfectly natural for Si).
I don't have as detailed an analysis for Se-doms, but it seems like brainheart summarized it pretty well with the tennis analogy. Se makes extremely quick associations, but when those associations are used in a non-physical, more intellectual context the exact same function is usually lumped in with Ne.
I absolutely believe that Ne is a valuable function and that many abilities come easily to Ne-doms that are more challenging for Ss (and obviously the reverse). I just honestly think it's often defined in a way that makes it indistinguishable from the other functions.