There is a distinct difference between etheric sight and astral sight, and it is the latter which seems to correspond to the fourth dimension.
The easiest way to understand the difference is to take an example. If you looked at a man with both the sights in turn, you would see the buttons at the back of his coat in both cases; only if you used etheric sight you would see them through him, and would see the shank-side as nearest to you, but if you looked astrally, you would see it not only like that, but just as if you were standing behind the man as well.
“Or if you were looking etherically at a wooden cube with writing on all its sides, it would be as though the cube were glass, so that you could see through it, and you would see the writing on the opposite side all backwards, while that on the right and left sides would not be clear to you at all unless you moved, because you see it edgewise.
“But if you looked at it astrally you would see all the sides at once, and all the right way up, as though the whole cube had been flattened out before you, and you would see every particle of the inside as well—not through the others, but all flattened out. You would be looking at it from another direction, at right angles to all the directions that we know.
“If you look at the back of a watch etherically you see all the wheels through it, and the face through them, but backwards; if you look at it astrally, you see the face right way up and all the wheels lying separately, but nothing on the top of anything else.”
Here we have at once the keynote, the principal factor of the change; the man is looking at everything from an absolutely new point of view, entirely outside of anything that he has ever imagined before.
He has no longer the slightest difficulty in reading any page in a closed book, because he is not now looking at it through all the other pages before it or behind it, but is looking straight down upon it as though it were the only page to be seen. The depth at which a vein of metal or of coal may lie is no longer a barrier to his sight of it, because he is not now looking through the intervening depth of earth at all.
The thickness of a wall, or the number of walls intervening between the observer and the object, would make a great deal of difference to the clearness of the etheric sight; they would make no difference whatever to the astral sight, because on the astral plane they would not intervene between the observer and the object.
Of course that sounds paradoxical and impossible, and it is quite inexplicable to a mind not specially trained to grasp the idea; yet it is none the less absolutely true.
— excerpt from Clairvoyance, by C.W. Leadbeater, [1899]