The two might be speaking of the same thing, but with different overtones. Say, a Klingon might find the idea of a "caste" of warriors demeaning, as it implies one is born into it rather than achieving status through one's own actions - so Antaak the Scientist might be deriding the warriors for their complacency, and insinuating that they are not properly earning their position in the society. There's clearly no love lost between himself and General K'Vagh.
On the other hand, there might exist a warrior class that consists of those born into it (the caste) and those entering it through achievements or twists of fate (the rest, with the sum total being the class). Again, Antaak might be indicating that General K'Vagh is from the hereditary "core" of the warrior class, although perhaps not in an insulting sense. Really, his delivery there might suggest he feels pity for the General...
The third option is that "caste" is wrong in every sense, and Antaak simply slightly mispronounced "class", or the quirky early Universal Translator made a mess of it.
Certainly it does not appear as if all Klingon warriors would be part of a caste, either in ENT or in other eras.
Timo Saloniemi