"Descriptive" vs "classifier" sounds like something made up to make learning easier.
I would be inclined to think more in terms of open compound nouns. You can't normally break up compounds, so the words have to go next to each other (like all rules, this rule can be violated for effect).
Compound nouns are nouns made of two or more words. They come in three types: "closed" meaning they have nothing between the words (blackboard, highlight); "hyphenated" meaning there's a hyphen between them (laughing-gas, daughter-in-law); and the ones we're interested in here, the "open" ones, which have a space between the words (tennis shoe, swimming pool, washing machine, living room, full moon, real estate, dinner table, coffee mug, African American, North America, bath tub, fish tank, bus stop, head teacher, grey matter, iron maiden)...
There is an infinite number of compound nouns, and whether they are open, hyphenated or closed has no real rule, though as a rule of thumb the more familiar the compound term is, the more likely it is to become hyphenated and eventually closed. Often all three versions are acceptable (ink well, ink-well, inkwell), but equally often, only one or two forms are OK.
Sometimes, open compound nouns become the first half of another compound noun, at which point they often get hyphenated: "washing-machine repairman", "African-American studies", "tennis-shoe holder".
Dancing shoes, educational reforms, political ideas; these are all just compound nouns. You can prefix them with any adjectives you like and not worry about descriptive and classifiers.
The first word of a compound noun usually gets the emphasis.
Now to answer your question: it seems like this emphasized first word of a compound noun is considered to be a "classifier", if it's an adjective.
I can see two ways to learn which is which. The first is to memorize every single compound noun... and there is an infinite number, so that's impossible. The second, is to get to recognize compound nouns, to recognize these word pairs where you'd emphasize the first word and the first word is a necessary part of the term. I think the latter is the way most people learn it, but I imagine it will be very hard when learning the language.
With a bit more googling, looks like these are using Halliday's systemic functional grammar (SFG) terms, and so will probably be useful in a study of functional grammar, but that really seems very esoteric for any ELL course. Reading his An Introduction to Functional Grammar, I see he writes:
A sequence of Classifier + Thing may be so closely bonded that it is very like a single compound noun, especially where the Thing is a noun of a fairly general class, for example train set (cf chemistry set, building set). In such sequences the Classifier often carries the tonic prominence, which makes it sound like the first element in a compound noun. [...]
Note lastly that a particular expression is a cliché does not imply that the modifying element is necessarily a Classifier. -- the 'permanence' is merely a feature of the wording! This in a considered opinion, a heated argument, the promised land, a going concern, the verbs are all Epithets"
Where he says 'cliché', I'd say 'open compound noun'. So seems I was incorrect above: a noun can be compound, and yet have its adjective not be a classifier.
I think, by and large, I disagree with this whole system of categorization. That said, let's try applying the rules he gives to distinguish them to these sentences.
The line between Epithet and Classifier is not a very sharp one, but there are significant differences. Classifiers do not accept degrees of comparison or intensity -- we cannot have a more electric train or a very electric train; and they tend to be organized in mutually exclusive and exhaustive sets -- a train is either electric, steam, or diesel.[...]
And later he writes (about verbs, I admit):
"an old political idea"
A very old, very political idea; an idea that is older and more political than another. That works. So are neither of these Classifiers?
I could not make an organized mutually exclusive, exhaustive set of idea types which includes "political", but I can for "old"; old, young, brand latest, obsolete.
The fact that the idea is all about politics apparently isn't relevant.
"latest educational reform"
The very latest, very educational reform; a reform which is later and more educational than another. That works. Again, I couldn't make a mutually exclusive, exhaustive set of reform types which includes "educational", but I can for "latest", as above.
The fact that the reform is all about education apparently isn't relevant.
"leather dancing shoes"
The very leatheriest, most-dancing shoes; shoes which are leatherier and more dancing than others. "Dancing" really doesn't work, there.
I could make mutually exclusive, exhaustive sets of shoe types based both on material, and on purpose.
The only one that's definitely a Classifier is "Dancing". "Political" and "Educational" both come across as definitely epithets by these rules, while "Old", "latest" and "leather" could count as Classifiers.
My advice: stick with my original suggestion about compound nouns, and it won't steer you far wrong. The other rules are very arbitrary and as we've shown here, give quite misleading results. Not to mention useless results. What's this meant to be teaching you, here?