By agreement from all participants the party has spoken with, these factions appeared as a result of the War in Heaven, a conflict which was instantaneous from the perspective of anyone outside, and infinitely long from the perspective of anyone inside. The Servants (essentially, sapient celestial beings) were originally split into two factions: those who upheld the One's divine plan for existence and Their order to never, ever use their powers to coerce mortals; and those who wished to uphold the divine plan but broke that commandment, using their powers, as well as simple force, to make mortals behave as desired. During the course of the war, a third faction arose, from members of both the Servants (loyalists) and the Fallen. This third faction came to enjoy the violence and destruction of the War in Heaven for its own sake, reveling in the feelings, the experiences, the chaos itself.
Representatives of all three factions claim that they won the conflict. Devils, whom the Servants call the "Fallen," believe that they won the right to prove that their way of doing things actually fulfills the One's plan, and that they only had to accept the minor inconvenience of actually being self-consistent; they see themselves as being tested and the demons (the "Destroyers") as their mortal enemies. Hence, unless celestial beings interfere with a devil's activities, they are quite content to not fight angels at all, seeing them as simply self-limiting siblings rather than outright enemies. Demons, aka the "Destroyers," believe that they won the right to slake their eternal thirsts and sate their insatiable hungers for as long as they like. They welcome the opposition of both the Servants and the Fallen, because that simply makes the task more interesting, more dangerous, more thrilling.
The PCs have only ever met one proper celestial being. The rest seem to be unwilling, or perhaps unable, to interact with the mortal world currently, though they have done so in the past. Specifically, the Safiqi priesthood began, a couple of thousand years ago, from teachings given by Servants, so the mortal church acts as their closest proper representatives. According to Safiqi doctrine, the Servants won the war, albeit at great cost. The One cursed both of the other two factions with what they wanted: the Fallen are now bound by the iron chains of the very law they wish to enforce on others, and the Destroyers are now enslaved to the very desires they wished to stoke, incapable of feeling satisfied.