For me, a Faction would be a section of society with a political foundation that would take Military action to display their views. An example being Crown forces, or the Kinshra. A Faction may not be vying for absolute control, but, for me, they would need to have an element of want - they would need to be politically influential, or attempting to become politically influential, and be attempting to put themselves in a position of power.
An Organisation, on the other hand, would either not be politically motivated (such as Avery Enterprises, which is a collaboration of Businesses emalgamised for the sole purpose of Industry by Brock Avery), or if politically motivated, it would not be materialistically involved, or if it was, it would not be vying for control. An organisation would not be in a place of power, however, a Faction would be, or at least, attempting to put themselves in one. Klaus Axis (talk) 02:17, April 8, 2013 (UTC)
I effectively agree with Klaus's explanation, with one point of clarification. All factions are organizations - however, not all organizations are factions. But yes, effectively, a "faction" is here used to indicate an organized party that has some kind of political or authoritative presence, esp. in the context of a militaristic force. SsVivid (talk) 02:49, April 8, 2013 (UTC)