While I think the terms Railroad and Sandbox are descriptive, they are awfully value-laden. They’re also the extremes: frequently a campaign with a strict story will have divergent paths and relevant choices, and a campaign with few demands on the player to follow the story will still have overarching plot and boundaries.
I suggest the following for campaigns more aligned toward the middle rather than an extreme on the player-choice axis, but still leaning toward one side or the other.
A Managed Play campaign is one where there is a significant predestined plot but players can make choices along the way that can affect the outcome. The DM probably writes an appendix to each adventure with plans for when players end up doing A, B, C, or D. There are several endgames, possibly with a point value from completed adventures or just eyeballing the result of the adventures up to that point. Or maybe it’s not that strictly pre-written, and the DM wants a result to happen for a major event, but the status of small events are entirely up in the air.
Managed Play is like a Disney amusement park. Everyone who comes thinks they can wander as they choose and experience the park however they want. But the park’s designers know how to build to regulate traffic flow and attract attention. You probably end up riding almost everything once and then grabbing dinner.
In a Managed Play campaign you draw all the dots (adventures, scenes, locations, whatever) and then connect them to form the plot. You flesh out the connected dots, but the ones outside the path you either don’t bother describing or give just a brief outline – because nobody will end up there.
A Distributed Play campaign changes things up by not connecting the dots ahead of time. The DM prepares a campaign without knowing what the players will do. His job is not to direct them to certain dots, but to make the dots known to the players so they can decide what to do. They may choose dots poorly (the adventure was to difficult for their level, or too easy and boring, or required some relic to complete that they don’t have yet). But the choice is theirs, and they may experience satisfaction at knowing their successes and failures are their responsibility.
A Distributed Play campaign can be played several times by different groups (or even the same group!) with dramatically different “story” results. This isn’t really possible with a Managed Play campaign. The players will be able to say “this is what we did during the Locust Wars” rather than “we did the Locust Wars campaign and ended up siding with A instead of B”.
Because it might not be obvious, it’s called Distributed Play because the adventures in the campaign are distributed around the map / timeline instead of just pre-planned, and also because the burden of decision-making for the story is distributed to the players more than in Managed Play.
This is just how I see the middle ground for the railroad vs. sandbox axis. I’m sure you all can come up with different possibilities. Personally, I suspect pure railroad or pure sandbox games are pretty uncommon, and most hover somewhere around these two. Also, the terminology is intentionally bland. If you can think of spicy terminology that’s not unduly positive or negative, you did my job better than I did. Or you could just use two positive terms, or two negative terms, but people will end up using the positive term for the one they like and the negative for the one they don’t.