Prior to the Faction War, the factions were relatively easy to define: They held some sort of power in Sigil, had a well defined belief system, albeit a system open to interpretation, and had a Factol who had a seat in the Hall of Speakers (as well as being listed as one of the 15 factions in the various PS books)...
After the Faction War, things changed...Some of the factions ceased to exist, some splitting into different factions (Mercykillers becoming the Sons of Mercy and the Sodkillers) and some combining with another faction to form a new faction (The Godsmen and Sign of One becoming the Mind's Eye), while some sects elevated themselves to factions (The Ring-Givers)...
My question is, if the old definition of faction is no longer relative, what is the new definition and what now seperates what is a faction and what is a sect?...Are the Harmonium and the Fated still factions, or have they downgraded to Sects as they are now primarily based on one plane?...
Kwint
Interesting question. The Harmonium and Fated are still much more numerous and powerful than most sects, I think.
Basically, a philosophical group is a faction if they're powerful enough to say they are (this is also the definition of a true tanar'ri).
However, the Harmonium and the Fated will both be expanding their operations in other planes now that their movement through Sigil is limited. The Fated will probably be building a headquarters in Yggdrasil, and the Hardheads might increase their use of spelljamming and the Labyrinthine Portal of Mechanus.
Also see Faction Secondary Planes at A Tiefling's Exultation.