The Ethereal Plane is another dimension, described in more detail on Pages 48 and 49 of the DMG. It may help you to replace the term "plane" with "dimension." The ethereal plane borders several other planes, and is often described as a muted, foggy outline of whatever exists on the plane that it borders.
So, take for example that you are in a corridor inside of Castle Ravenloft. There is a spot in the ethereal plane which looks exactly the same as the castle corridor, except it's all fuzzy looking and grey and foggy. Any creature on the ethereal plane is invisible to the stuff in the castle corridor, but the creatures in the corridor are visible to the ethereal denizens. Creatures on the ethereal plane also feel no gravity, and can move through walls easily.
The ethereal plane is used very often then for travel, as well as espionage, since travelers can move through walls, as well as spy on people on the material plane without worry of being discovered. Ghosts and other such incorporial undead can move into this plane at will (which is what allows them to turn invisible).
If a character can use true sight, they can see into this plane. So if anything is spying on them using this plane, they will see it. They can also see ghosts and other such spirits that try to hide from them by moving into this plane. They will also see things that were hidden in the ethereal plane for safe keeping.
As for the effect of this on your campign, that really depends on how much you use alternate dimensions as a DM. If you don't use the ethereal plane for very much, the spell just means that the PC can follow ghosts and other such things, as you have noted. If you like to put spies in there, or other such hidden things "stashed away in the fourth dimension", then the PCs will notice those things. The effect is pretty minimal, since your players would acctually have to shift themselves into the ethereal plane in order to affect anything you put on that plane.
As noted by Andrewk, Ravenloft is filled to the brim with trapped ghosts. Even if they don't directly interact with the players, it can be a powerful narrative/aesthetic device for the PCs to see so many souls in the ethereal plane as they move through the castle.
That's a 20th level epic boon (so very powerful)
The power of a permanent truesight effect would be situational. If you measure 'power' by raw combat ability, then unless you're fighting invisible creatures truesight has little effect. Even if this player is fighting invisible monsters, the rest of the party is still vulnerable. So it shouldn't break combat balance. Outside combat, truesight would also be of little use if you don't encounter illusions or shapechangers or ethereal creatures, although if you do encounter those things it solves those challenges trivially, which may be an issue for the DM trying to make interesting challenges. The range would also be a big factor. Truesight to a range of 10ft (for instance) requires the player to be standing very close to the item of interest and wouldn't be as powerful as a range of 60ft, which would reveal an entire room.
But if we want to see how powerful the ability of permanent truesight is in general, we can look at where the game designers have made truesight available for player characters. You have already noticed truesight's availability as a 6th level spell, which automatically puts it in a rather high echelon of power. But where would permanent truesight fit into the picture?
The answer is found in page 232 of the Dungeon Master's Guide, under Epic Boons. Epic Boons are only available to player characters who are at level 20 and are made to extend the power of already-powerful 20th level characters. Of these epic boons, there is one which provides exactly the effect you are considering:
Boon of Truesight
You have truesight out to a range of 60 feet.
If the game designers thought that permanent truesight (to 60ft) is something worthy for only a 20th level character, you should be very cautious with giving out a similar ability to a lower level player character. Putting a much shorter range and/or limited uses per day might (might) help balance it for lower level characters, although it will still be very powerful in certain situations.
Best Answer
They convey the same information in this secenario. You correctly interpret that True Seeing grants you a range of 120 feet., and that Truesight enables you to see into the Ethereal Plane within the specific range that is 120 feet.
A common game design idea is to make information available that faces the person who needs it. The text of Truesight is GM facing and the text of True Seeing is player facing — see that Truesight appears in the BR chapter 12 part 4 Dungeon Master's Tools about the senses of Monsters. So while the information itself is redundant it accomplishes an emphasis that maybe isn't as obvious as the other aspects of what Truesight grants the player. Did the editor use that principle, or did they miss it? We don't know, and the editor probably doesn't remember anymore.