This concept frequently comes up when I explain this idea to my friends, so I'm primarily writing this so I have a convenient place to link them the next time I have to explain it.
first rung: 'useful'
The levels of my hierarchy are essentially systemic safety nets; anything that falls through the first level is tested against the second level and so on. The requirements get progressive more lax to cast the net wider and wider.
At the first level, we must ask ourselves 'is this convention useful'. This is the highest, strictest and most salient level, dealing with all 'important' conventions. Here, we have Newtonian Mechanics, folk theories of mind, most (vertically transmitted) religions, etc.
The property of interest here is that while these cultural inventions really (in the Chapman sense of 'really' denoting 'in some sense') reflect structures in the real world. The gotcha here is that things first go the a homomorphism-distorting utility calculus.
I'll unpack that last bullet of jargon. A homomorphism is an algebraic equivalence which essentially means a isomorphism that preserves structure. A function like x^2 or 7x map most xs onto different numbers than themself (that is, 3 becomes 9 or 21, 7 becomes 49, etc.), it preserves several useful relations, such as the total ordering '>'.
It has been neatly demonstrated (Quanta article, paper) that, generally speaking, homomorphism-preserving internal representations of the external world, i..e. beliefs structures that accurately map reality, are not evolutionary viable, particularly when computations are expensive (i.e. always).
And this captures the 'utility calculus' part of it as well; the distortions is caused simply by the fact that usefully non-homomorphic representations are generally 'better' than their undistorted alternatives.
But I digress. It's be instructive to point to things that are patently not in this category. These are Quantum Mechanics/General Relativity, the consensus neurology/psychology/sociology, etc.
second rung: 'accurate'
The next level catches anything which isn't useful per se, but accurately respects reality. Everything I mentioned at the end of the last sections falls here.
You might have noticed that the first rung is relative; generalizations like 'bigger brains mean higher intelligence' are useful when describing populations and averages, but hopelessly imprecise for describing individual people. In fact, accuracy becomes usefulness whenever the domain of interest is scientific.
The second rung is equally nebulous in a distict way; where what is 'useful' mutates whenever the domain of interest changes, what is 'accurate' varies as time. As the canonical example of this: Newton's Mechanics was accurate centuries ago, but not now.
third rung: 'convenient'
This is an even more nebulous rung. 'Convenient' is anything where you can do it anyway you want, but some ways are just plainly easier. In linear algebra, you can describe vectors by translating your vector space by any constant amount you like, and the calculations are equivalent. But still, A translation by +2,-8 or 0,+5 are much more convenient than (say) +(pi),-sqrt(3) or -e,+8/9.
I'd guess the main thing making this a distinct category from usefulness is that for usefulness, you can do it a different way, and you get a different answer. GR gives slightly different answers than NM, (and by the accuracy criterion is slightly different in the right way), but there is a reason we use NM for things like mundane trajectory calculations, and we'll define that reason by that and denote it 'usefulness'.
Likewise, there is a reason we do our calculations in base ten rather than base three or base phi, and we'll define the reason by that and denote it 'convenience'.
fourth rung: 'convention'
This is finally where everything has fallen through and any framework is neither especially useful, especially accurate, nor especially convenient. This is the domain of ISO standards, certain cultural artifacts, whether we spell it 'color' or 'colour'.