I think Illusionism applies whenever the GM negates player choice in such a way that the players don't know it has happened.
Hmm.
I think you're using "illusionism" a little differently than others in this thread, but I understand what you're saying.
The only qualification I'd add is this- rarely do these issues come up in such simplistic ways. Its not as if I'm out there telling the pcs, "You spring down the hallway, fleeing the guards! But oh no! It branches! Which way do you go, left or right?" and then sending them to exactly the same room no matter which way they choose. In that sort of case, I wouldn't branch the hallway at all.
Really, there are three bits of DMing practice that get attacked as denying player choice, when I really think that they're just wise dungeon mastery. I'll explain by example, using things that come up when I DM.
First
The PCs are investigating a mystery. There are three primary clues which, once gathered, will solve the mystery. There are three secondary clues, which lead to encounters during which the PCs will uncover the primary clues. So all told there are a minimum of six scenes which will have to happen for the PCs to solve the mystery.
The PCs enter the first scene. The clue they need to uncover here is that Lord Schmoe is cheating on his wife, which will let them interogate his mistress, who will turn out to have witnessed events important to the mystery. That is, Lord Schmoe is an encounter that provides a secondary clue, which leads to an encounter that provides a primary clue.
So, they're questioning Lord Schmoe. Unfortunately, the PCs bomb their skill checks.
Everyone agrees that the adventure shouldn't end here. That would be lame.
The question is, what should be done?
What I'd do is provide some other way that the PCs could uncover the secondary clue. Perhaps a servant lets slip some detail. Perhaps they spy on Lord Schmoe and see him meeting his paramour. Perhaps one of the other staging encounters where secondary clues are uncovered involves someone who lets slip a detail that sends them back to Lord Schmoe, this time better prepared to catch him in a lie. They can come up with whatever they like, or else I'll queue them with something. Either way, eventually they uncover the secondary clue, and the adventure moves on.
Now, some people say that this makes it so that success or failure "doesn't matter," because you get the clue either way. To these people I would respond: You are insane. Its like saying that a football game where one side sets an early lead and maintains it the whole game is somehow "the same" as a game that is neck and neck, with each team pulling ahead momentarily only to fall behind again, with one team finally squeaking out a victory. It doesn't matter if both games end with the same team winning.
The way it happened is important. Roleplaying games are similar. No one would say that it "doesn't matter" whether you fight zombies in a crypt or battle pirates on the high seas, even though both routes might lead your character to advance a level. The journey inherently matters.
Second
Imaginary World A: In it, I am preparing for a session. I know that I have a player character in my party who can cast the hypothetical ritual "Speak With the Dead." So, I put an important clue in the mouth of a dead NPC, knowing full well that the PCs will find it.
Imaginary World B: In it, I am preparing for a session. I consider giving an important clue to a dead NPC, but then reject that plan, because I suddenly remember that none of my players chose to create a character with the ability to cast rituals, so such a clue would go uncovered.
Some people have argued to me in the past few days that this is a bad decision on my part. They have claimed that I am somehow making the decision of whether or not to take Ritual Caster meaningless, because the PCs get the clue either way. Again, to this I say: You are insane. If you truly mean this argument, you are telling me that my only proper course of action is to... to what, exactly? Put the clue in the unfindable location anyways, so that the PCs can fail to find it, thereby making their decision not to take a feat into a meaningful one? That is crazy. I submit that not even the people who are making this argument actually run their games that way.
Before you call the above two arguments straw men, they're... not. They might be responses to unclearly stated positions, but if that is the case, the fault lies with the unclear positions, and not with my response to them.
Third
This is the only one on which I'm prepared to give even the slightest ground.
We'll use a generic example.
The PCs are headed for an encounter. This encounter is expected to be tough, but the PCs do not know its exact constituent components- ie, they don't know exactly what monsters they'll be fighting or under what conditions the fight will take place. I don't either, as the DM- its a few sessions out, so I haven't written the details yet. I know a few generalities: it will feature the Big Bad Guy, his lieutenant, and a bunch of his allies. It will be difficult. But it won't be impossible. Probably player character level +3 or something.
Now, the PCs come up with a clever plan. This plan will kill off the lieutenant before the encounter. They enact the plan, and the lieutenant is killed.
Now its time for me to write the actual encounter. I have a choice. I can create a player character level +3 encounter that includes the lieutenant, and then delete him, and have the PCs fight what's left. Or, since this is the climax of my campaign, I can write a player character level +3 encounter that doesn't include the lieutenant, and run with it.
Some people believe that choosing the latter makes the player character's choices meaningless. They killed the lieutenant, and the final fight "didn't change." They ask, "why come up with the clever plan at all, if the DM is just going to make things harder to put you back where you started?"
To them I have several responses.
1. Things DID change. The fight would have had a lieutenant. Now it doesn't.
2. The journey still matters. Killing the lieutenant DID have an effect- it advanced the plot line. That's part of it, too. Things which help write the game's plot line matter, even if they don't have a direct effect on mechanical matters.
3. It should really bother you that the logic of whether or not I've made my PCs decisions meaningless
changes based on how far in advance I plan. There's a weird Schroedinger's Effect in this reasoning. I can instantly make this not a railroad by not having firm plans about the Big Bad Guy and the Lieutenant both being present in the final battle.
4. If a railroad is absolutely invisible, intangible, silent, odorless, and impossible to detect or interact with in any way, is there really a railroad? The PCs don't know how exactly tough the final fight was going to be. They don't know that it would have been the Big Bad, his Lieutenant, and 6 mooks, and that now its the Big Bad and 8 mooks. Maybe the plot line I had planned was one where the PCs would have been overpowered and possibly forced to retreat, but now they won't have to thanks to their efforts. Maybe the plot line was one where I expected the PCs to come up with plans to weaken the bad guys before the Big Fight, and I intentionally planned the Big Fight to be impossible without some sort of plan before hand. Who knows? The players have no way of knowing the answer to that. They just know what they see, and what they see is no railroad at all- there were a number of enemies arrayed against them, they killed one of them, and now that one's gone and they can fight the remainder.
5. The entire concept of trying to look into the DMs mind and determine what would have been, and then arguing that the PCs have been denied meaningful choice based on what the DM might have done if things had been different, is highly, highly questionable. If I was going to make a hallway branch, with two possible outcomes based on each branch, as mentioned at the top of this post, and then I decided not to bother and made the hallway a straight, unbranching line, have I denied the players a meaningful choice? I guess you could kind of argue that I have, but I'd argue that my denial itself wasn't meaningful. Or at the least, that this argument proves too much- it would imply that every time I could have added a choice to the game, but didn't, I was denying my players meaningful choices. Every second I don't spend fleshing out my campaign world therefore becomes an attack on player autonomy. This line of reasoning gets outlandish fast.
I'd argue that instead the only forms of "denying player choice" or "railroading" that really matters are 1. forms the players can tell are happening, and 2. forms that do so in a way the players don't enjoy. If those two criteria aren't both met, no one has any reason to complain. And in real life, as opposed to this forum, no one WILL complain.