Here's why I tend to disagree if it matters. In the end it's just creating or identifying temporary aspects - doesn't really matter what we call it. However, Fred states it better than I do.
This got ranty. TL;dr. It matters because of the way you come up with Target number, and Declarations are inherently better for Thaum.
Actually it kinda does matter if you're adjudicating based on the book. A maneuver is a target of, I believe, 3unless opposed. A declaration, between 0-6, and an assessment(worth noting do to the link) anything up to the GM's discretion. It seems Assessments are just maneuver to discover GM truth, giving it a different target value. The opposition is the GM's fiat, as opposed to an opponent rolls.
So if it's an action of some type the PC is doing, to affect(effect?) the scene, they only need to hit a 3, unless opposed. If it's them discovering something already there, it's a whatever the GM decides. If it's something the PLAYER, decides should be in the game, it's between 0-6.
As Thaumaturgy isn't really supposed to get a scene, maneuvers are out. Plus, any actions being done are supposed to be them creating the spell. The "Maneuvers" that you would normally set up are all the prep that happens off screen. So that leaves Assessments and Declarations as ways of generating aspects. But assessments are actions and furthermore, just GM opposed maneuvers, so they are out too. That leaves declarations.
You can't have a navel gazing moment as a declaration though, because a declaration isn't an action. It's a truth about the world. The declaration might be, I declare I have the money and contacts to but the uranium needed for ghost dust, but it's still not the action of going, finding the seller, and buying it. It's nit picky, but it still seems like an important bit of pedantry (yes yes, I know, oxymoron). It's important because of the difference in what target number the Player is shooting for, but also in the way it is determined. There is no rule that enforces interesting behavior on a Maneuver. Such a rule does exist in declarations. If it's a really boring aspect, lets take the navel gaze equivalent declaration, it will be a difficulty 6.
"My character is a master magician and can focus for days at a time for no food. So I want the aspect. Mind like David Blaine"
Well, that's boring, stupid, and leads nowhere. So it's a target 6. Roll your discipline
If it's a really interesting aspect, it will be a 0
"I'd like to have the stolen the wedding ring of the finger of a powerful witch 6 years ago."
Well shit, that's awesome. 0. Roll your burglary. Or deceit, or stealth. That's so awesome I don't care.
But what if they have a 5 in that skill so they can make 6's easily? Well, You can shut them down out of hand, "You already made your shitty discipline declaration, Try for something with a little more jazz" But maybe that's not your style. Personally, I hate saying no. So instead I'll say, yup. and then make their house explode before they have time to cast the spell. If they aren't going to be interesting, be interesting for them. Either way, use the guide as way of judging declarations. If they are coming up with 0 and 2 difficulty declarations, the story is probably benefiting from it. If they are making 4-6, then you know the story is getting boring at it's time to do something else.
The point being, Declarations provided a way of measuring how valuable the contributing aspect is to the story, with an incentive to make it more interesting. Since Thaumaturgy is inherently boring to RP, use the system that mitigates that by design.