The terms “Apollonian/Dionysian” are derived from the names of the Greek gods Apollo and Dionysus. Apollo was the messenger of the gods, and the presiding deity of music, medicine, youth, and light, and was sometimes identified with the sun. Dionysus was the god of vegetation and wine and, it might be said, of ‘permissiveness’.
Friedrich Nietzsche used the terms in The Birth of Tragedy out of the Spirit of Music (1872). He was making a distinction between reason and instinct, culture and primitive nature; possibly brains as opposed to loins and heart. Apollonian is also often thought to signify ‘sunny’ and ‘serene’, whereas the Dionysian means ‘stormy’ and ‘turbulent’. Nietzsche argued that these elements formed a unity in Greek tragedy where dialogue provided the Apollonian element and the dithyrambic choral songs the Dionysiac. In the 19th c., this antinomy was much elaborated, particularly in the work of Schopenhauer, but it was Schiller who originally made the distinction between naiv and sentimentalisch.
Among more modern writers D. H. Lawrence was deeply interested in it. He might be described as a Dionysiac writer whereas Stendhal and André Gide were Apollonian. Of course, a combination is possible, as in Shakespeare’s sonnets, or the love poems of John Donne and Robert Burns.