I don't like the term "illusion of choice" or "railroad" for my style, even though I can see how people might think that's what's going on.
The players don't get a choice in what major story beats are going to happen, which NPCs they meet and what set-piece encounters they experience. They do get a choice in what context they meet these people, where they are when they experience the major story beats and how to engage with the set-piece encounter.
For example: In my last session I wanted three things:
the PCs to get some face time with the BBEG of the next little arc (a Dr. Mingel), (meet an NPC)
have a chase scene through the busy streets of London during the day and (set piece encounter)
have Dr. Mingel attempt to obduct an NPC (Mr. Fairstyle) that could become a major source of power to the PCs (story beat).
So a regular questgiver gave the PCs the task to find and protect this Fairstyle character (hook). How they go about this is their choice. But whatever they do, once they rolled two or three times successfully to find Mr. Fairstyle (be that through asking around amongst their contacts, using divination magic, or digging through the church register to find Mr. Fairstyle and his antecendants), they will get a solid clue to his location. He can be found in a public place where scandal is to be avoided. Once there, they find Mr. Fairstyle and Dr. Mingel already engaged in polite conversation, which they can join. They observe behaviour in Dr. Mingel that reveals him to be a bad guy. When leaving the public place either Mr. Fairstyle or Dr. Mingel will attempt to flee from them (depending on context and who they try to chase).
All of these things will happen. All of the details are up to my players. E.g. I did not know ahead of time that Mr. Fairstyle and Dr. Mingel would be in a Casino playing a rare card game that is only offered in this one place. It was a casino with a specific card game because thats what the trail of clues led the PCs too and the 3rd successful roll was when talking to a gambling guy who had met Mr. Fairstyle before (I hadn't fixed the number 3 before either, that was purely based on how much time they spent searching and what the mood was at the table, if we had gotten caught up in throwing back Monty Python quotes for half an hour a single roll would have sufficed and if the players were really into the investigation bit it would have taken them 5 or 7). The players decided to chase down Dr. Mingel when exiting the casino and leaving Mr. Fairstyle to fend for himself. So while they caught Dr. Mingel, his henchmen caught Mr. Fairstyle and while they try to get him back, (spoiler alert) Dr. Mingel will escape in their abscence.
Edit: Btw, they had killed a previous incarnation of Dr. Mingel without learning his name or talking to him. So the dead guy is now Dr. Mingels dear but insignificant assistant, for which he also wants to kill the players (long term). The story beat they hit there was "disrupt one of Dr. Mingels operations", and the set piece encounter was a fight in a warehouse full of chemicals. I would have liked it if "Dr. Mingel" had gotten away from that fight (in which case they would have recognised him in the casino), but "learn the BBEGs name" was not on the agenda for that session so they don't even know that they 1st turn killed the BBEG of an entire story arc. Because they didn't because that wasn't Dr. Mingel because that's not the context the players created.
I don't like the term "illusion of choice" or "railroad" for my style, even though I can see how people might think that's what's going on. The players don't get a choice in what major story beats are going to happen, which NPCs they meet and what set-piece encounters they experience. They do get a choice in what context they meet these people, where they are when they experience the major story beats and how to engage with the set-piece encounter.
For example: In my last session I wanted three things:
So a regular questgiver gave the PCs the task to find and protect this Fairstyle character (hook). How they go about this is their choice. But whatever they do, once they rolled two or three times successfully to find Mr. Fairstyle (be that through asking around amongst their contacts, using divination magic, or digging through the church register to find Mr. Fairstyle and his antecendants), they will get a solid clue to his location. He can be found in a public place where scandal is to be avoided. Once there, they find Mr. Fairstyle and Dr. Mingel already engaged in polite conversation, which they can join. They observe behaviour in Dr. Mingel that reveals him to be a bad guy. When leaving the public place either Mr. Fairstyle or Dr. Mingel will attempt to flee from them (depending on context and who they try to chase).
All of these things will happen. All of the details are up to my players. E.g. I did not know ahead of time that Mr. Fairstyle and Dr. Mingel would be in a Casino playing a rare card game that is only offered in this one place. It was a casino with a specific card game because thats what the trail of clues led the PCs too and the 3rd successful roll was when talking to a gambling guy who had met Mr. Fairstyle before (I hadn't fixed the number 3 before either, that was purely based on how much time they spent searching and what the mood was at the table, if we had gotten caught up in throwing back Monty Python quotes for half an hour a single roll would have sufficed and if the players were really into the investigation bit it would have taken them 5 or 7). The players decided to chase down Dr. Mingel when exiting the casino and leaving Mr. Fairstyle to fend for himself. So while they caught Dr. Mingel, his henchmen caught Mr. Fairstyle and while they try to get him back, (spoiler alert) Dr. Mingel will escape in their abscence.
Edit: Btw, they had killed a previous incarnation of Dr. Mingel without learning his name or talking to him. So the dead guy is now Dr. Mingels dear but insignificant assistant, for which he also wants to kill the players (long term). The story beat they hit there was "disrupt one of Dr. Mingels operations", and the set piece encounter was a fight in a warehouse full of chemicals. I would have liked it if "Dr. Mingel" had gotten away from that fight (in which case they would have recognised him in the casino), but "learn the BBEGs name" was not on the agenda for that session so they don't even know that they 1st turn killed the BBEG of an entire story arc. Because they didn't because that wasn't Dr. Mingel because that's not the context the players created.