Yes, Kierkegaard makes much use of the distinction. He directs his criticism toward Hegelians in that vernacular. It is ironic, however, that the distinction has a psychological dimension that is often employed in Hegel.
One place where Hegel is directly challenged by Kierkegaard is at the beginning of The Concept of Anxiety.
Thus by captioning the last section of the Logic “Actuality” one gains the advantage of appearing to have reached the highest, or if you prefer, the lowest, through logic. The loss is, however, obvious since neither logic nor actuality is served thereby: not actuality since contingency, an essential ingredient in actuality, is something that logic cannot let in; and no good is done to logic since if logic has thought actuality, it has ingested something it cannot assimilate, anticipated something for which it merely prepares the way [prædisponere]. The penalty is clear: every deliberation about what is actual is held back, yes, and perhaps for some time made impossible, since the word “actuality” must first be given time to as it were come to its senses, time to forget the mistake.
–Kierkegaard, Søren. The Concept of Anxiety: A Simple Psychologically Oriented Deliberation in View of the Dogmatic Problem of Hereditary Sin, translated by Alastair Hannay
The ensuing “psychological deliberation” will use some of the language developed by Hegel but within limits that correspond to our limits. Accordingly, Kierkegaard addresses the idea of movement in Hegel’s Logic:
What will follow now? Presumably language will come to celebrate a great sabbatical year† in which speech and thought take a rest so as to begin with the beginning. In logic the negative is used as the quickening power that brings movement into everything. And movement one must have in whatever way one can, by fair means or foul. The negative helps, and if the negative cannot, then wordplay and platitudes can, just as the negative itself has become a play on words.* In logic, no movement may come about, for logic is, and everything logical simply is,† and this, logic’s impotence, is logic’s passing over into coming about, where human life [Tilværelsen] and actuality step forward. So when logic gets absorbed in the concretion of the categories, what was at the beginning remains constantly the same. In logic every movement, if for a moment we are to use that expression, is an immanent movement, which in a deeper sense is no movement, as one will easily convince oneself by reflecting that the very concept of movement is a transcendence that can find no place in logic. The negative, then, is the immanence of movement, it is the vanishing factor, what is annulled.11 If everything happens in this way, then nothing happens at all and the negative becomes a phantom. But precisely in order to get something to happen in logic, the negative becomes something more; it becomes what produces opposition and not a negation but a contraposition. The negative is then not the muteness of the immanent movement, it is the “necessary other,”12 which may no doubt be most necessary for logic in order to set things going, but which the negative is not. If we leave logic and proceed to ethics, here again as in the whole Hegelian philosophy we find the negative indefatigably active. To our amazement, we find that the negative here is the evil. Confusion is now in full swing, there are no bounds to brilliancy, and what Mme. de Staël-Holstein13 has said of Schelling’s philosophy, that it makes a person clever for a lifetime, is true in every way of the Hegelian. One sees how illogical the movements in logic must be, since the negative is the evil, and how unethical they must be in ethics, since the evil is the negative. In logic it is too much, in ethics too little. If it has to fit both places, it fits nowhere. If ethics has no other transcendence, it is essentially logic; if logic is to have as much transcendence as ethics requires to preserve common decency, then it is no longer logic.
–ibid. (pp. 39-40)
From this basis, Kierkegaard goes on to establish the limits of psychological explanations as they relate to the problem of the single individual and the consciousness of sin.