Something I've been noodling around in my brain for a bit is a better description of Map and Key play, which I do find to be a very apt description of trad play and nicely illustrates the differences. And, yes, I absolutely, resolutely will NOT use the word "guess" anywhere in my little essay here. I've learned my lesson.
Description of Map and Key
In M&K play, the point of play is that the GM creates what is essentially a flow chart - sometimes with hard lines between nodes (dungeon crawl) or sometimes fairly soft ones (hexploration) but the point is, the GM creates these nodes which correspond to the key on the map and each node is something "interesting" for the players to interact with. ((Note, I'm painting with a fairly broad brush here, so, yes, I am perfectly aware that exceptions exist - like random encounters forex)) The players, in this style, start from a point of very little information and then explore the map/flowchart in a heuristic way until they have uncovered sufficient information about the map to call it finished. Either they've sufficiently "cleaned out" the dungeon, achieved whatever goal(s) they had or maybe even just decided to go in a different direction for whatever reasons. The point is, the point of play is to explore that map. The DM is constrained by the map and key to not start making unreasonable changes (quantum ogres) because that renders the goal of exploration problematic. While the flowchart might be dynamic (nodes change over time), changes are made in a logical manner which could be revealed to the players and the players would be perfectly fine with the changes. So, the orcs in this location move to that location because they wanted to reinforce that location's inhabitants would be perfectly logical and understandable and no one would object. Spontaneous Orc generation simply to make the encounter harder likely would be objectionable. (although not always)
Non-Trad Play
Now what differentiates non trad play here is that exploring and revealing the map/flowchart is not the goal of play. Often play doesn't even have a keyed map at all. If it has a map, it's more likely vague and generally only used as a sort of general framework rather than the point of play. Players aren't there to explore that map. They are there to explore these characters. Encounters aren't so much challenges to overcome but rather opportunities to further define character. Players are given far more authoritative control over the setting than in M&K play in order to facilitate this different exploration.
I dunno. It made more sense in my head as I was noodling around about it. But, to me, that really highlights the difference between these games. They are both about exploration of a kind, but, the type of exploration is and goals of that exploration are very, very different. Which means that players and game masters really have to shift gears in order to traverse between one style and the other.
IMO, where things get all fouled up is when one insists that the way you play one type must work in the other type of game. And it just doesn't. It can work, if you are willing to do a LOT of yeoman work to kitbash it together, but, the end goals of the different games really means that it's probably far more work than it's worth. Not always. After all, the old 007 game was fairly traditional in it's approach - map and key, that sort of thing. But, it also had Bond Points, (I think that's what they were called) that let the players make changes in the game in order to make them look and feel more like 00 agents. So, that Russian Spy DOES fall for my (incredibly cringe) pick up line for example. That sort of thing.
So, there can be cross pollination, but, at it's heart, the two styles of games really are quite different.