I think there's a very fuzzy line between a linear campaign and a true railroad. So my definition of one versus the other may differ a bit.
To me a linear campaign has a set number of events and obstacles that can potentially be approached or bypassed, but must in some way be overcome. There is a specific predetermined goal but details on how you get there is up to the party. A true railroad dictates how you overcome those events and obstacles.
I try to run a game that's a linear sandbox in that I don't know exactly where the game is headed and people are absolutely allowed to go left instead of right or thwart an opponents plans through clever play. But there's always a clear direction to go, clear goals for the party to achieve because that's what my players ask for.
Which is to say that there is a broad spectrum of styles of play and there's even quite a bit of variance in what people would consider a railroad. Modules are almost always linear and if someone is running a module I know what I'm signing up for. It's just about the only thing people are willing to run so when I do get to play I just accept that it's what I'm going to be doing and go with the flow.
In the same way, convention and game day modules are more on the railroad side of the linear spectrum. But I still enjoy them because I enjoy seeing different DM styles, meeting and playing with new people, getting new perspectives. I get to just sit back, likely talk in a funny accent with a character that is writ large in broad easily recognized brushstrokes. I don't have to worry too much about analyzing motives or deep moral dilemmas (which are far too often badly handled "force the PCs to choose between two equally evil options" anyway). I can just sit back, have fun, make bad jokes and roll dice.
My definition differs a bit.
To me railroading is when nothing you say or do matters to the outcome. This applies equally to illusion of choice or blatant railroading.
Illusion of choice is when the DM presents you with two doors and informs you that one leads out and the other is one way deeper into the dungeon. Then no matter which one you choose, you end up through the door that leads deeper into the dungeon. The choice was illusionary and you are just doing what the DM wants you to do.
A blatant railroad is when you come to a wall and you try to climb over it and get informed it's unclimbable. Then when you want to fly over a strong downward wind keeps you from being able to rise. And so on. The DM is doing this because he wants you to go down the passage and kill the Jabberwocky first.
I view illusion of choice to be the worst of the two. The DM is lying to me in order to waste my time forcing me down his path. I'd much rather see the railroading so that I can decide whether I want to stay in the game(which might happen if it's with friends) or leave the game.
Where my definition differs from yours is that the obstacle may have multiple ways to be overcome. The DM doesn't have to dictate the method. Only force you down the path. In the Jabberwocky example the DM might have dropped clues to the Vorpal Sword being hidden nearby, but be open to other methods of defeating it. Then once dead the magical winds suddenly vanish and/or handholds appear on that wall enabling you to now go in that direction.
Sometimes it's kind of nice just to shut off your brain and enjoy playing.
That's called just being a player. Man, when I can stop DMing and just play, it blows my mind how much easier it is. I don't have to worry about a bunch of NPCs, their goals and what they know, juggling four PCs, knowing what's happening in the world, answering questions, etc.
It doesn't take linear or railroad to shut off my brain and enjoy playing. It just takes me not being DM.
