As it’s known from the Effigy Shield description, the occult rebellion that Velka seems to have played a big part in has failed:
"In an ill-fated plot to destroy the very gods, the followers of the occult once attempted to steal the power of Gravelord Nito, the first of the dead."
It is possible that after her plots have been found out, Velka was banished or fled to the Painted World of Ariamis and Gwyndolin (perhaps secretly) took over the covenant, after which Velka started the legend of the Chosen Undead that would allow her to take worthy undead warriors from the Asylum into Lordran and have them mercilessly attack and destroy the gods she's been warring with.
In Japanese mythology, crows are seen as servants of the gods and are often sent out for divine intervention in the world of mortals. In this vein, it can be speculated that the giant crow that transports the Chosen Undead to Lordran is a servant of some god, and given Velka's obvious connection to crows it is safe to say that if that were the case, then the giant crow serves (or is her).
Gwyndolin, to counter the legend, attempts to manipulate the Chosen Undead into his own cause instead, that of linking the First Flame. To support this, consider the following evidence:
Gwyndolin, leader of the Darkmoon Covenant rewards the player for killing the half human, half crow hybrids associated with the worship of Velka, found in the Painted World of Ariamis. These crows drop Souvenirs of Reprisals:
"The knights called the Blades of the Darkmoon punish the guilt-soaked offenders of the Gods and take this as proof of their conquest. The earless corpses of the guilty will be left behind as a warning to others, inspiring both fear and respect for the Gods."
Such is the eternal mandate of the Dark Sun."
The punishing of the "guilt-soaked offenders of the Gods" is the mandate of Gwyndolin, not that of Velka. Gwyndolin seems to be using the Darkmoon Blade covenant to manipulate the Chosen Undead to kill Velka's followers and hunt those who oppose the gods:
"O Disciple of the Dark Sun. Thou hast journeyed far; hear my voice.
If thou shalt swear by the Covenant, to become A shadow of Father Gwyn and Sister Gwynevere,
A blade that shall hunt the foes of our Lords;
Then I shalt protect thee, safeguarding thy person with the power of the Darkmoon."
"Very well. Now thou art a Blade of the Darkmoon. Hunteth the enemies of the Lords, by the power of the Dark Sun."
Furthermore, Gwyndolin's Darkmoon Talisman allows its user to use sorceries with faith instead of intelligence, while Velka's Talisman enables the user to use miracles using intelligence instead of faith, they are the exact opposite of each other, further demonstrating a significant difference between how the two leaders operate:
"[Velka's Talisman] casts miracles not by drawing upon faith, but intelligence."
"[Darkmoon Talisman] demands dutiful faith from its owner, but has very high miracle adjustment."
This is further supported by the apparently different motive on the Blue Eye Orb and Black Eye Orb:
"These mystical [Blue Eye] orbs are granted to Blades of the Darkmoon, knights who serve the Dark Sun Gwyndolin, so that they may serve the Gods in meting out vengeance."
"Mystical [Black Eye] orb found on a Keeper's corpse. Invade the world of the murderer of a Fire Keeper, to defeat the perpetrator and reclaim the soul of the Fire Keeper. The Black Eye keeps constant watch on the city of the Gods, Anor Londo."
The desciption of the Vow of Silence, miracle of Velka might have been used as a precaution against Gwyndolin, him being a magic caster himself, while other gods being known as miracle users:
"Secret rite of black-haired witch Velka. Prevents casting of magic within effect area."
After killing Gwyndolin, Oswald, a pardoner of Velka has unique dialogue, seemingly congratulating the player for killing the leader of the Darkmoon Blades, which seems unfitting for someone who supposedly serves the same cause:
"Good tidings, thou art welcome. Laudable is thy dedication to sin."
Cut content reveals that there may have been a covenant devoted to Velka, tasked with hunting down the Blades of the Darkmoon, which would imply that Velka and Dark Sun Gwyndolin were in fact enemies.
