It's my stance that there's only one form of player agency.
The artificial division is about an accepted limit to player agency which people don't want to admit is a limit, even though they're pointing out that what they want and expect from play relies on that limit.
Affecting the world through PC actions is not the same as the player authoring stuff without the PC being involved at all. 1 =/= 2.
Well, your post said that your google search turned up two types of agency, character and player agency. If character agency is that which is limited to a player being able to declare actions for his character... then player agency would seem to be what I'm talking about, no? How the player can influence the direction and outcome of play, aside from character agency.
I didn't think that's what you'd be advocating for, since every game I know that supports what you're calling player agency also supports character agency... and would therefore support more agency than a game that only allows character agency.
The more of one you have, the less of the other. There's only so much time during a game and you can't be doing both all the time. Further, the focus of your games is different, so character agency takes a huge hit. You guys don't focus on the "boring" stuff PCs do and instead do character testing stuff.
Since the amount of time is the same(ie 4 hours for your games is the same as 4 hours for mine), you can't have more agency than my games do. You either have yours and I have mine, or you break yours and mine up so that it totals 100% and mine is also 100%.
Oh I'm sorry, I figure that rather than staring at each other like idiots, the GM would put the living world to use to do one of the things it's great at... have the world go on even when the PCs don't do anything. So that threat they ignored? Now it shows up. The gnoll pack they did nothing about has now hired some giants, and they attack the town. What do the players do then?
If nothing is happening, it's not just the players who've failed.
It's comments like this that prove just how little you understand what we are saying. Or more likely, you don't bother to try and understand, because you just said that you figured that in less than 10 seconds of game time, living world stuff would happen gnolls running off to hire giants and then getting those giants to attack town. All in 10 seconds!!!
Maybe you run your game as absurdly as that. But I don't.
If nothing is happening in a sandbox game, it's because there are no proactive players. You also clearly don't read my posts before responding to them. For once in your life, try reading to understand instead of reading to reply. It will save you from typing ignorant stuff like that paragraph above this response, because I said that if they stare like that, I initiate something to get things moving along, but that it's no longer a sandbox if I have to do that.