Something never stuck right with me about the Headshot effect we see when we kill Fallen, which we are officially (I think) supposed to take as their souls venting from their bodies. We know that at least one Archon's soul was preserved and held in a prison, and was then reinstalled into a body just in time for us to fight him. What we have seen of these souls, and their venting from a Headshot, they're visibly "Light" of some sort, in contrast to the spooky green and dark vapors of Hive deaths when they evaporate from their husks. That the Fallen are able to persist beyond the death of their bodies, and come back again, and that they may be infused with Light - at least of a kind - might make them very similar to Guardians.
So that gets me wondering - were the Fallen the Traveler's original Chosen people? Is that from where they "fell" and became The Fallen? Though we never hear from them, it might be safe to presume it's a name they have accepted and adopted; the Queen of the Reef refers to them as Fallen and she commands their respect, and must necessarily have respect for them in turn to have assumed the role and responsibility from the Kell she defeated.
"The Fallen" may be an honorific title to them, as they broke away from the Traveler and became the Traveler's enemy. They may take pride in their revolt and chasing him across the galaxy to continue their war on the Traveler, using what they've learned and gained against the Traveler.
The Fallen were the First Guardians.
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*slow claps as the Speaker comes out of the shadows* You've finally figured it all out, Guardian...or should I say...Fallen. XD