The unity of Apollon and Artemis, quite easily explained by those orphic hymns which call Misa (clearly derived from the name of Artemis as a daughter of Demeter) as the double Euboleus (Apollon as the swineherd son of Demeter fulfilling his character elsewhere in connection with this mysteries as a herder/leader and of a nature parallel to that expressed by Diodoros Siculus as the chorus-leader of Dionysos/Osiris) expresses the nature of Apollon and Artemis as deriving from the same source…mythically the womb of Leto. As such Apollon and Artemis have naturally reflecting features of their domains, which likewise carries over into a great number of shared or closely related epithets. Though they have distinct functions and personalities, they are inseparable and cosmically linked for that even as Artemis drives the prey in her hunt, Apollon receives what she had hunted. Thus establishing a never ending pattern of energy and the effect of the energy under control. Artemis hunts forth, and Apollon destroys. Even in their cult centers it is difficult to find the presence of one without the other.
Of course the masculine-feminine dichotomy is presented here a bit different than it has been presented with other such cases in which you have myths of a divine source being separating into another, usually the case of a male separating himself into a female. She is still part of him, and he is still part of her, but they are at the same time separate. Usually in such cases when this arises in which you have a male and female deity of the same source they will be bonded together in a marital or procreative relationship. However in the myth of Apollon and Artemis these twins fall into a different relationship that follows its cultural expression. Romans seemed to have attempted to modify the tones of the relationship a bit in the retelling of the story of Orion in which Apollon, jealous of the relationship between his twin and the hunter, tricked his sister into shooting him in a contest. Yet such jealousies in regards to the twins rarely crop up, though they are quick to defend each other and act for each other, as Artemis struck down Coronis.
Yet, there is something that ties into their relationship that reflects a reaffirmation of their unity in a vein similar to the procreative elements, and that lies mostly on the part of the maidens loved by Apollon. This is particularly the case when we see his first love, Daphne. This nymph was for all intensive purposes identical to the nature of Artemis. She too was a huntress who hunted with a band of fellow nymphs throughout Peloponnesius. Likewise, the wife of Apollon, Kyrene is also a double for Artemis in her persona and character. She too is a huntress/shepherdess who disdains the womanly arts to tend to the wilds. In fact, she was so closely associated with Artemis that she was said to have been given dogs by the goddess for her hunt. Of course there are figures who are less like Artemis with whom Apollon carries on a brief affair, but these two maidens figure prominently in his myths in Hellas, and Kyrene is the only marriage that he has had in myth, with full honors by the gods via the presence of Aphrodite creating for them their marital bed.
For Artemis there is a case, retold my Apollodorus in his the Library, in which according to an alternate version of the story of Callisto that the maiden was seduced by Zeus not in the form of Artemis, but rather in the form of Apollon. Herein we have the form of Artemis being replaced distinctly by that of Apollon. That Callisto would permit herself to be embraced by Apollon in substitution for Artemis suggests that the lines are easily blurred between what Artemis is doing, and what Apollon is doing and that for one of her followers to be embraced by Apollon was of quite a different nature than the same action being performed by another god.
I would like to reiterate that this post is not intended to say that Apollon and Artemis are one and the same in all ways, but rather that they are a male and female components of a whole for which we see too Apollon also called hunter like his twin, and Artemis as Despoina carrying on her lap the staff, likely of the kind which a shepherd would use that is aligned to the staff of Apollon Karneios. So they dance together in their cosmic actions. They do not need to be procreative, and in fact it is not necessary for their actions. Apollon is the destroyer at the boundary/gate, Artemis is the nurturing lady of the portal/doorway the huntress who drives forward all things through life. They do not need to be procreative together to do their parts harmonically as twin lights of the same function. Just their unity is brought home between the points of their twinship, and the character of the bride of Apollon. It is merely illustrated in this fashion through myth.