A fallen angel is an angel that has turned away from the Light. While the precise meaning of the phrase differs from fanfic to fanfic, the general concept of abandonment of paradise/rebelliousness against authority hold true.
In some themes they are the equivalent of demons.
Aeon of the Champion (AoC Universe)[]
In the Aeon of the Champion story series, fallen angels are completely dissimilar to demons, having a very different place of origin. Fallen angels in this fanon originate from the High Heavens but have turned renegade and gone against heavenly orders. A classic example is Lucithel, the Lightbringer, who betrayed his brethren during Antiquity after an intense argument with Duterius turned into an all-out brawl in Mezarel's Court of Justice, with the fight only adjourned after Anariel intervened and used her power to imprison them both.
Pandemonium is a common location for fallen angels to go, out of the sight of heavenly dogma and reach of hellish chaos. There they are joined by all sorts of sinister and shady creatures, from half-breeds to monstrous aberrations. Lucithel did this after his betrayal, and brought the Urori to bear on both angels and demons before deciding his defection was complete.
Fallen angels usually consider themselves above both good and evil; whereas angels are 'white' (good) and demons 'black' (evil), fallen angels are a shade of grey. Some emphasise the need for compromise/third-way, and others reject the binary altogether.
The creator of the series considers himself a 'fallen angel' in the sense that he is morally ambiguous.