Darjes is an 18th century author who published Introductio in Artem Inveniendi, seu Logicam theoretico-practicam, qua Analytica atque Dialectica... (1732). He assigned todefined the analytic as the "science of rules for discovering truths with certainty" and dialectic as the "science of discovering plausible truths". The "discovering" part separates him from contemporary Wolffians, who saw logic only as ars demonstrandi, and anticipates the understanding of Logic (and dialectic in particular) in later German idealism.
To the analytic Darjes assigned "concepts and definitions and their origin either a priori or a posteriori, judgments and sentences, intuitive judgments and the generality a posteriori, discursive judgments..." and to the dialectic "probability in general and and as a way to dialectically find the truth, a way to find apparent terms or definitions, theoretical sentences a priori and a posteriori, philosophical hypotheses, hermeneutic probability, probable criticism, assessment of the likelihood of other people's opinions".
Kant has two types of analytic and dialectic, formal and transcendental. In both cases the division is between correct and incorrect employment of understanding and reason in their formal (general, syntactic) and transcendental (synthetic, semantic) functions. On Kant's "transcendental dialectic" there is more or less an agreement, see e.g. IEP, Kant’s Dialectic, Loparic, Kant's Dialectic, Guyer, The Unity of Reason and Rotenstreich, Kant's Dialectic.
It is the antithetical "logic of illusion" ("a sophistical art of giving to ignorance, and indeed to intentional sophistries, the appearance of the truth, by the device of imitating the methodical thoroughness which logic prescribes, and of using its "topic" to conceal the emptiness", A61), but of a special kind. It has to do with the tendency of pure reason to employ concepts of the understanding to unify knowledge beyond the boundaries of experience, and thereby fall into antinomies and "transcendental illusion". The reason preoccupies itself with directing understanding "towards absolute totality in the synthesis of conditions", which can never be guaranteed to terminate, but then transgresses into positing such absolute totalities as transcendent objects, as if this synthesis of appearances has already terminated. That's the transcendental dialectic. Here is Loparic: