The linear adventure vs sandbox debate

Both linear and sandbox elements have their place within D&D, and that place is going to depend heavily on factors like length of campaign (a true sandbox one-shot is borderline untenable), what the current campaign plot requires, how much guidance players need, and DM comfort. Even within a sandbox campaign, you might have linear moments (a quest line that the party might have trouble leaving), and linear campaigns can have sandbox moments (any good heist might be linear in goal, but should give the party a sandbox of break-in options).

On the topic of railroading, I think Davyd nailed the technical definition.  The only thing I would add is a secondary definition of “pejorative used by players to inaccurately describe a linear game.”  I think that is a misapplication of the term, but it is a frustratingly pervasive one and is worth noting as its own definition.

I also think it is worth noting that, while the term is negatively charged, there are times railroading is beneficial to the function of the game. Often, those are going to be moments like keeping the party on track for what the DM prepared (The_Ace_of_Rogues mentioned this on the first page), putting a problem party member in their place above table, or helping to avoid red flags for players.  If your player is going to say “I want to ignore the main party’s quest and go off and do a solo mission with my Dragonmarked house” or “I want to torture the prisoner even though a player said torture made them uncomfortable” those are acceptable times to pick the player up and place them back on the rails, briefly forcing them to ride the DM’s train instead of their own.  Generally speaking, the goal here is to railroad as minimally as possible - the DM keeps them on the rails until the problem junction has passed.

I think there are also places for more soft railroading.  Less forcing a person to ride the train, and more making sure they see the tracks.  “Hey, I think you did not pick up on this clue, here’s information you have as a character that really suggests this course of action” or “That plan could work if everything goes well, but your characters would recognize those are high level mobs and if things did not go perfect, you’d have a split party and likely die.” 

Ok, from a player standpoint, i am good with almost anything as long as I am told what it is, and if a switch up is coming, that i know to start instigating at the right moment instead of waiting for story.

From the DM perspective, some people are better at one than the other and they need to find their strength.  Because i have sat through enough sessions of one type of DM trying to pull off the type they aren't good at to know that they can be really boring if they don't play to their strengths. 
Once had an open world DM try to play a Linear campaign and he didn't do a great job because he thought too ridgedly to make up for his open world tendencies. So it was A-B-C-D then then he got flustered when we figured out D too fast and took steps that headed off E and F and would have taken us to G.