Well here's the thing... there's like a zillion different fields intersecting, and they're not really all the same even if related. What social groups you hang out, what your motivations are, how you think, what you cognitive values are...

I suggest taking a look at the overall philosophy of what NiTe in socionics is all about, and once you really internalize the philosophy behind that cognitive valuation, see how it relates to the stuff like being businesslike.

In my own conception, a good number of Jung's original prophet types were probably ILIs, and I don't think business-like is the way to characterize their Te. But more or less the way they seemed to work is that their intuition discerns the overall context of the time they're involved in, and often their focus was more on proclaiming the activities relevant to be done in that context than in developing logical frameworks to capture a static intuition - the nature and importance of the idea would tend to shift with context much more greatly, so there wasn't as much of an impetus to define it as is. The attitude to judgment was definitely that it is secondary, so some would be scant on rationalizing the activities they proclaimed must be done.

So I'd basically just view the social groups fitting in stuff as more of a (possible) result of the cognitive valuations, and understand what NiTe vs TiNe is getting at.