That's why I used the quotes...I don't know of accepted terminology for the playstyles in question. If there are such terms, people don't seem to use them.

I've seen other people get offended by "Wuxia" or "Anime". If you have another suggestion, I'm all ears.
You know, I really don't know if there even
is good terminology for this. Any kind of shorthand one-word description would probably end up with problematic connotations or would lead to differing interpretations from different people. "High-powered," "flashy," or "cinematic" are possibilities, but I don't think any of those alone are ideal. This really is a source of difficulty in talking about this kind of issue, isn't it?
Assuming there is a middle ground, sure. However, as you mention above you can do both as once (and maybe a third or fourth style of high-level play.) I suspect we need more of a neutral ground, rather than splitting the difference. What does that neutral ground look like for higher level play? What implications (if any) does it have for lower level play? Do certain spells or abilities need to be restricted to higher levels by default?
This is a very good question. I'll need to work my way through this a bit...
If we start from low level play, it might be a bit easier. At low levels, I'd say it isn't too hard to start off with three common types of play and one uncommon type, as I mentioned in a previous post. There is "default fantasy", where groups of heroes fight monsters and have a perfectly reasonable chance of surviving, but don't do much flashy stuff. There is "gritty fantasy", where people fight monsters and have a pretty poor chance of surviving. There is "flashy fantasy", where heroes do
cool stuff and have a good chance at surviving. And finally there is "gritty, flashy fantasy", where people both do cool things and tend to die a lot. Gritty fantasy I would associate with optional mechanics like more dangerous healing/wounding rules, weapon degradation, a chance of instant death in almost any attack (though not necessarily random), and so on. Flashy fantasy I would associate with more complex mechanics designed to make characters seem more awesome like stunt rules, action points, fancier powers, and so on. Default fantasy is simple, and flashy/gritty fantasy just combines both aspect of those rules. It's not perfect, but I think this idea touches on a lot of key playstyle differences.
Now, as for how this translates into higher level play... For the most part, I think the same spectrum of grittiness and flashiness applies. Grittiness brings more possibility of death, and flashiness brings more options to avoid death. High-level grittiness favors things like Save or Die spells, and high-level flashiness favors things like "Once per day, when you die" tricks. High-level default lacks either for simplicity's sake, and high-level gritty/flashiness has characters bouncing back from save or die attacks with their "when you die" defenses.
Something like becoming a king or ruling a stronghold would be rather unrelated to that spectrum, I believe. Such a thing would probably be rooted in the same mechanics as hiring mercenaries and servants to assist in dungeon exploration, which could come into play at very low levels. I suppose this would be a third optional element to the game that could be layered on to the default or on to the other options.
I guess this gets back to your question of "what does the default look like at higher level play?" I guess the answer would be that it is simple, compared to other options. It would lack many character options provided by those other modules, so characters would have fewer class features (maybe?), but the mathematical baseline would probably be the same. Wizards would have fireballs, Fighters would make attacks, and so on. I suppose the thing about a stripped-down default is that it wouldn't be all that remarkable in any particular way, other than that it would be quick and easy to run.