I encounterd this typology when reading Jung, but it is derived from Nietzche. here is what the Wikipedia page says on this:
Nietzsche's aesthetic usage of the concepts, which was later developed philosophically, was first developed in his book The Birth of Tragedy, which he published in 1872. His major premise here was that the fusion of Dionysian and Apollonian "Kunsttrieben" ("artistic impulses") forms dramatic arts, or tragedies. He goes on to argue that that has not been achieved since the ancient Greek tragedians. Nietzsche is adamant that the works of above all Aeschylus, and also Sophocles, represent the summit of artistic creation, the true realization of tragedy; it is with Euripides, he states, that tragedy begins its "Untergang" (literally "going under," meaning decline, deterioration, downfall, death, etc). Nietzsche objects to Euripides' utilization of Socratic rationalism in his tragedies, claiming that the infusion of ethics and reason robs tragedy of its foundation, namely the fragile balance of the Dionysian and Apollonian.
Apollo (Apollonian or Apollinian): the dream state or the wish to create order, principium individuationis (principle of individuation), plastic (visual) arts, beauty, clarity, stint to formed boundaries, individuality, celebration of appearance/illusion, human beings as artists (or media of art's manifestation), self-control, perfection, exhaustion of possibilities, creation, the rational/logical and reasonable.
Dionysus (Dionysian): chaos, intoxication, celebration of nature, instinctual, intuitive, pertaining to the sensation of pleasure or pain, individuality dissolved and hence destroyed, wholeness of existence, orgiastic passion, dissolution of all boundaries, excess, human being(s) as the work and glorification of art, destruction, the irrational and non-logical.
The relationship between the Apollonian and Dionysian juxtapositions is apparent, Nietzsche claimed in The Birth of Tragedy, in the interplay of Greek Tragedy: the tragic hero of the drama, the main protagonist, struggles to make order (in the Apollonian sense) of his unjust and chaotic (Dionysian) Fate, though he dies unfulfilled in the end. For the audience of such a drama, Nietzsche claimed, this tragedy allows us to sense an underlying essence, what he called the "Primordial Unity", which revives our Dionysian nature - which is almost indescribably pleasurable. Though he later dropped this concept saying it was “...burdened with all the errors of youth” (Attempt at Self Criticism, §2), the overarching theme was a sort of metaphysical solace or connection to the heart of creation, so to speak.
The Wikipedia page also gives other definitions, such as those of feminist author and cultural critic Camille Paglia and in linguistics.
Camille Paglia writes about the Apollonian and Dionysian in her book Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson . The two concepts split a set of dichotomies that create the basis of Paglia's theory. For her, the Dionysian is dark and chthonic while the Apollonian is light and structured. The Dionysian is associated with females, wild/chaotic nature, and unconstrained sex/procreation, while the Apollonian is associated with males, clarity, rationality/reason, and solidity, along with the goal of oriented progress. Paglia attributes all the progress of human civilization to males revolting against the Dionysian forces of females, and turning instead to the Apollonian trait of ordered creation. The Dionysian is a force of chaos and destruction which is the overpowering and alluring chaotic state of wild nature, and the turn away from it towards socially constructed Apollonian virtues accounts for the prevalence of asexuality and homosexuality in geniuses and in the most culturally prosperous places such as ancient Athens.
Others mentioned include science fiction writer Robert A. Heinlein, Ruth Benedict, Thomas Mann, Hermann Hesse, singer Jim Morrison, literary critic G. Wilson Knight, Ayn Rand, and horror writer Stephen King.
I might also add Stan Gooch's polarity of System A and System B, the Tantric symbolism of sun and moon, or pindgala and ida nadis, and obviously the Chinese polarity of yin and yang