The difference is that I can choose to place my character under orders or in circumstances that limit my future reasonable actions to essentially a linear sequence of events. Note the reasonable. There is always a choice. Many linear situations in reality that the alternative is so unpleasant or so not fun that it is ruled out.
The other way that gave rise to the term in the first place is imposed by out-of-game fiat.
Whether players have fun with a style should not be the determining factor of whether it is a
different style or not.
The group can happily choose to play a campaign that they know is going to be a linear series of events because they agree beforehand not to stray from the "path".
The difference is not whether one is happy about it, it is about whether it happens because of out-of-game fiat or whether it is something choosen by the player acting as their character in the campaign.
Whether the players are on board for it or not should not be the determining factor of whether it is a different style or not.
These are just more refined ways of saying the players are happy about it. In the previous section, it is whether the players find it
reasonable (meaning, they accept the justifications; they would balk, aka be
not happy, if the justifications were insufficient). In this section, it is whether the players have
consented to it or not...which means they're having fun,
which means they're happy.
Like...you are literally saying that it's a different style based on whether the group is on board, vs not on board. That's not a stylistic difference. That's a question of
group acceptance.
Now, you could argue that "railroad" is
supposed to be a term only for
badly-handled linear campaigns/modules/etc. That's not presenting "linear" and "railroad" as completely different things, but rather saying that railroads are a (poor-quality) subset of linear campaigns/etc. And the main rebuttal would simply be that it doesn't really matter whether that's what the term was "supposed" to be for, because people actually use it to describe what you call "linear" campaigns/etc. all the time: campaigns/etc. that require that players be willing to not make choices that point outside of the pre-planned content. And others
understand it similarly.
Of course it's true that "railroad" has some...baggage, shall we say. But it's also a useful metaphor. Sort of like how WoW-type MMOs are often called "theme park" games, because it's like going to Disneyland or whatever. You can only ride the rides so many times (on a given trip, anyway) before you've basically seen and done it all. Yet millions of people go to them all the time (pandemics notwithstanding), while the contrasting option (not-so-coincidentally also called "sandbox") is metaphorically a dime a dozen unless the people playing therein bring something special, or the sandbox itself offers something that can't be had elsewhere (e.g. Minecraft, though it's not really an "MMO" proper.)
This is wrong. It's not about what the players choose. It's about the set up of the adventure. If you have to go to A, then to B, then C, then D, etc. in order to get to the next step, the adventure is progressing in a line. It's a linear adventure. Contrast that with an adventure like Isle of Dread, which you can finish in many different orders and without going to every spot to be done with the adventure.
It isn't any shape other than a line. It's literally A-Z in a line. It's the only way the players can finish it. If they decide to finish it.
...then what makes it different from a railroad?
You're literally saying that the only choice the players have is to
stop playing the game. That's literally the one and only choice offered by a railroad. It's not like the DM can somehow trap the players in her house for each session!