WHAT EXACTLY IS A DUNGEON?

It's where you find dragons.

I think Unity has got it pretty much right, it's a sense of danger and risk, with a reward of some kind for traversing it. To use a real world example, when I was growing up I literally had woods at the bottom of my garden, my home backed onto the local forest. I'd go walking through them on a regular basis without coming to harm, but the wood was home to a large variety of wildlife, some of which was territorial. I knew to avoid certain areas at certain times of the year especially around mating/birthing season because you really don't want to be to near animals in rut or ones protecting their newborns. I was never harmed but a few of my friends who weren't as observant or were just unlucky came away with damages a couple quite serious. I wouldn't consider those woods to be a dungeon, even though there was a level of danger there for the unlucky or unwary.
In contrast near where I live now there is a cave system which is well known for being the habitat of a particularly nasty and venomous breed of snake. If I went in there no matter how careful I was I'd be running a fairly high risk of being envenomed. It is however the shortest way to get to a really lovely scenic spot that is perfect for picnics, which is why some people use it as a short cut even though the longer way is safer. So it has danger, risk and reward. Dungeon material in my mind.

It's where plot happens.

Let me explain. I have a similar situation where there is no world map, players just move from map to map and generally don't backtrack. Most maps have monsters on it as well as puzzles, but they aren't dungeons because the story's events don't happen there. They exist to get players to the dungeons. Let's take an event very early in the game- a bandit chief is kidnapping children and holding them for ransom in a cave. The heroes go to stop him. The walk through the field to that point isn't considered the dungeon even though you might encounter bandits along the way, the cave itself is because that's where the story unfolds and you fight the bandit chief. Then again, we associate "cave" with dungeon anyway, so I have another example- a corrupt town.

Let's say the heroes arrive in a town that starts out fine but we learn the leader is actually corrupt and evil. At night the heroes need to sneak in and fight him, taking out guards on the way. The town is then turned into a "dungeon" because there's a significant amount of story unfolding there, even if during the day it was just a normal town.

My way of looking at is is this:

Is it some form of obstacle or challenge (whether puzzle, or enemy, or both) that the player has to surmount, with some end goal (whether it's to just get to the other side, to kill the boss, or just to loot some chests)?

Then it qualifies as a dungeon in my book.

When it ceases to be a challenge to be overcome and becomes a commute, as LockeZ alluded to, then it stops being a dungeon.

In Zelda 1 and 2, those dungeons existed to get players to the triforce at the end, in the same way that a field on the way to a bandit cave exists to get players to the bandit cave at the end. That's exactly the same amount of "plot."

It's not the same type of plot though, even though it sounds very similar when simplified to that degree. I think what you're actually trying to get at is this: the player's goal is inside the dungeon, not beyond it. The player has an objective at the end of the dungeon. This is a legitimate idea. An area that you are passing through on the way to somewhere else can definitely feel less dungeon-like for this reason.

Rather than arguing any more about semantics I think I want to look at this idea from a different perspective.

What aspects of this kind of field map cause it to not feel like a dungeon, and how does each of those aspects change the way the player plays or feels? Going down the topic so far:

The player is safe.
Without battles, the player's experience is obviously extremely different. Battles in RPG are the primary form of gameplay, and they're also what make your choices matter during exploration. Usually, the longer you explore, the more battles you get in, whether that's because you wanted to track down all 40 treasure chests or because you got lost. Without these battles, a typical map lacks any reason to not fully explore every cranny.

The player doesn't have to overcome challenges to progress.
Without battles, there's nothing interactive on the map except for treasure chests which are all in plain sight and easily accessed. There's no barrier whatsoever to progress. Therefore it can easily seem like making the player walk through it is just a waste of time. If it's absolutely guaranteed that the player will make it through the area, and getting the treasures is also basically guaranteed, why make them spend time doing it manually? If your map were filled with complex puzzles, or had a time limit or something, it would probably work better - without that, the exploration is going to be extremely boring.

The area doesn't stand on its own.
This area replaces the world map, and a genre-savvy player is going to be acutely aware of this fact, while a novice player will get a subconscious feeling that this is clearly not where the action happens.

The area is a path, not a destination. As a result the player will think about it differently. It feels less climactic. Less important. The player expects it to be simpler and easier. It won't get the player's complete focus. Because their specified goal in the area is simply to "get out of the area," they will be much more likely to see the entire dungeon as simply an obstacle to progress in the game, and will be anxious to move on to what they consider the next real dungeon.

There isn't a boss.
You can have a dungeon without a boss, obviously, as you can have a dungeon without most of these things. But it certainly feels somewhat less like a dungeon. Having a climactic end gives the player a good sense of accomplishment when they complete it. You're obviously not going to have the same sense of accomplishment if the player didn't accomplish as much. But more than that, having a big finale feels good, even if having three more normal battles might've actually been harder. I think the boss fight itself is almost a ritual to some players, a celebration for completing the exploration part of the dungeon.

It's outdoors.
This seems so minor. It affects the player's mood though. The area feels less oppressive. The player doesn't feel boxed in, even though the area might be mostly linear. Sometimes this is what you want. Sometimes it's not. I would say this has more effect on your storytelling than anything else. If your characters are on the run, in hiding, tossed into a prison dimension, etc., that feeling of openness is something you probably want to avoid. If your character is travelling on a grand adventure across the world, on a journey with no immediate goal at the moment, that openness is something you probably want to cling to.

I like unity's definition "an area where the player isn't safe and must overcome challenges to progress". I like nhubi's IRL experience with mating forests and snake dungeons (lol). And I like LockeZ's definition of what a dungeon is, by defining what it is not. He also pointed out his decisions very logically, which I like as well.

author=nhubi
That's it Cash in your RMN game I want to see either a mating forest or a snake dungeon, or both. :)

Why not go all in and make a forest of mating snakes? XD