How Do You Handle the "Inside" of a Hex?

Hey! if you were linked here from elsewhere, this version is outdated. Please read this one instead.

[EDIT: I've replaced this post because it's not very good. When I wrote it, I was idly spitballing about a pattern I thought I had maybe picked up on, without much thought. It's unfocused, poorly articulated, and lacks confidence or authority. Worse yet, it's also filled with mistakes, many of which have been noted by others over the years. Lastly, it ends with a bizarre departure into me talking about my own crappy homebrew stuff. I would delete it, but many of my colleagues strongly object to that. Preserving the blogosphere for posterity, yadda yadda. So go read the new version instead.]

I have noticed an unspoken disparity in the way people seem to use hexes in the context of a hexcrawl, and I think it deserves some attention. That is: do you bother with precision in the movement that takes place within a hex OR do you treat the space within them as fairly nebulous and concern yourself only with the movement between hexes? I'll explain the difference, and I'll also talk a bit about "sub-hexes" later. And if anyone has seen discussion of this somewhere already, then please point me in that direction.