The issue is not black and white and you will not find a concrete definition because each developer is different and most do not classify their games as such. Depending on who you ask you may get a few hundred answers on what type of game or experience defines each term, here is what it really boils down to and what most who have been around can agree on.
Sand-box: Player generated content in which developers give the community/players tools to create content and interact, shape, and change the game world around them. Most MMOs in the last ten years do not follow this model and most games in general do not follow this model.
-SWG in part, was one of the bigger "sandbox games" as you could create content in some forms in which players could interact with, the game world was also so vast that you could run in a single straight line for hours and never reach an "end" (Invisible wall). Exploration, or the lack there of, does not make a game sandboxy or not, remember that the word comes from playing with toys in a sandbox. It is what you make it out to be.
-Minecraft is the most popular sandbox game out and people do not even realize that it is. You create what you want, the world populates it with NPCs and blocks to build or deconstruct and the fact that you can run in the game forever (Until Java kills it) and see random generated content. If an MMO was built just like that it frankly would be pretty boring.
Theme-Park or On Rails gaming is what you have come to expect from games these days. Developers spend years crafting quest lines and stories in a logical progression model in which you grow as a character and play in their world. Most MMOs are like this in nature because people want structure they want a path of progression that is easily followed and understood. If a developer built a world and then just dropped you in, level one, nothing else you would probably quit after a few hours. You are strapped into the game world that the developers create, you have limited to no tools to change and shape that world in a permanent fashion. Could you siege a city? Sure, but its going to reset after a while and in the grand scheme of things does not make a difference at all.
Just because the world has invisible walls does not mean it could not be a sandbox game and vice versa.
First off,
I've been around since the beginning of time (so to speak) I remember when pong came out.
Pong is the "beginning of time" for home video games, incase you didnt know?
Without a concrete definition.
Nobody can ever say anyone else is wrong, Which has happened in this thread (as well as others) many times over.
On rails gaming (as you put it);
Is not what someone expects from the Elder Scrolls series.
Prime example; enter a dungeon (either on a quest or not) Finish 50% turn around and walk out of that same dungeon.
On rails example; To even enter dungeon you MUST be on a quest and that quest MUST be completed to exit the dungeon.
logical progression model the Elder Scrolls way;
I've maxed several characters levels in Skyrim without even starting the quest line Bethesda worked years crafting.
(You'll find many players of the Elder Scrolls series have done the same or close to it.)
And each time I played the game I ran into people/things/places I'd never encountered before.
May not seem a logical way to some to create a game but personally I think its brilliant.
Drop you into a world level one;
They pretty much did just that with Skyrim.
Take whatever path you want after getting out of Helgen & even encourage you to do so via dialog with an NPC
This line after reaching the world coming from an NPC ring any bells? "Probably best if we split up"
Your choice at that point, follow them or take the advice he just gave you and split up.
Quit after a few hours, why? Games like this is what keeps me playing them after all these years.
BTW no need to explain other game models or games, got a pretty good understanding of them honestly.
Theme Park on the other hand, just say linear design.
i.e. Once on the roller coaster your not getting off until the rides over. linear
linear is not something Elder Scrolls ever has been and should never become.
(but yes, like any video game there must be some linear aspects to it. They just dont work otherwise)
Bottom line is, Until people have actually played the finished product nobody knows what TESO will really be like.
If the whole things "on rails" I'll personally only play a month & then cancel.
Open world/free roam the way Elder Scrolls is ment to be, I'll be around awhile.
Gonna be like WoW or other current MMO's (with the exception of WWII online)
I'm wasting my time even reading this forum, Not interested in the finished product at all if thats the case.