I can't help on the Aristophanes, but I did a lot of work on Greek and Roman theology in my honours year.

While Greek mythology (as reported by the poets) and civic religion (as practiced in state cults) was conspicuously polytheistic, natural philosophy has a long tradition of veering in the direction of monotheism.

Platonists and Stoics tended to view God as a highest, greatest, most perfect being, and thus by necessity he is singular. While there is a "one-ness" about this God, these groups of philosophers also for the most part believed in the conventional deities as well. Xenophanes made the earliest surviving reference to this kind of pagan monotheism: "One God, greatest among gods and men, in no way similar to mortals either in body or in thought..." (Clement, Strom., 5.109.1)

Following from this, Plato often refers to a singular, highest "God" as a supreme deity. In his Timaeus he talks about the creation of the universe and how it was set in motion by this one greatest God, who is the uncreated first-mover. Later in Plato's creation narrative, God made the conventional gods, who in turn went on to create people and animals.

Greek texts of the classical period did not capitalise words (papyrus scrolls of literary works were essentially written in all caps). Greek also likes to use definite articles ("the") in front of proper names, which feels foreign to English speakers.

In most modern translations, editors choose to translate ὁ θεός as "God" if writer was referring to a Supreme Deity in a philosophically-monotheistic sense, and render the same phrase as "the god" in other contexts. (In older translations, the conventional polytheistic gods may also be transcribed as "the God" with a capital G; early modern printing standards generally favoured more capitalisation than today's standards.) Since the purpose of translating is to convey the sense of words in the original language as effectively as possible in the target language, it would be misleading to label a philosophically monotheistic deity as "the god", and equally fumbling to label one deity in a pantheon as "God"; therefore, both phrasings need to be used depending on what concept is implied.