: "Class" does not exist, except as an abstract concept. Neither does "race". These are merely tags one uses to group people into sets, frequently in an arbitrary manner. The value of this grouping lies less in any real political analysis, and more as a targeting mechanism. Thus:
: I am race "X". You are race "Y". By virtue of this distinction, I will make claims on you, backed up by violent force, for debts I will arbitrarily claim from you. These might be debts owed for civilizing you, or for enslaving you, but they are held over you because you have been designated as a member of that set. (Usually, the "indebted" set is chosen because it is weak, and because it has wealth, labor, and/or property worth expropriating).
: As with class: You are wealthy. You are thus a member of the "wealthy" or "capitalist" (Jew? WASP?) class. You have the ability to pay, and are in the minority, and so will be forced to pay the debt owed for owning money. This will be in some proportion to your wealth (most states), substantially in excess of that wealth (socialism, where not only property but earning potential is expropriated), or all your wealth, and your life as well (Bolshevik communism and, to a lesser extent, Nazism).
: This set dispersal is no more applicable to a scientific analysis of social activity than is placing all slow moving, meaty animals that are not vicious into the set of "jungle foilage exploiters", thus explaining predatory behavior in terms of a righteous indignation focused against such creatures.
: This, simply put, is why Marx was "wrong", i.e. in justifying murder and theft in the name of justice and fair play. Not that the new "judicial class" is altogether concerned.
You describe class simply as the internal description of that class. A "tag" as you put it. But no analysis of anything can be performed without context. Class, as used here, is not simply the 'class of blue-eyed teenagers' but a derivative of social relationships. In other words, it is the way these social relationships are organized that defines class. The organized 'rules' of slavery will produce one set of classes. The organized 'rules' of capitalism will produce another, etc.