>Factions is a term that refers to what most players are accustomed to calling "Race" or sometimes more vaguely, "Army"; but is perhaps better interpreted as "Codex". Imperials is -not- a Faction. Adepta Sororitas, Astra Militarum, Imperial Knights, and each type of loyal Space Marine are all individual Factions; for instance.
>The only time this is of particular import is when you are building a Battleforged Army; as your "Combined Arms Detachment" (what we recognize as the standard FOC) must consist of units only from a single Faction (codex)... or, alternatively, -no- Faction. (an option that I suspect will become available somewhere down the line) Savvy?
>Furthermore, your "Allied Detachment" (which is identical to what we know already) must include units only from a single Faction, and that this Faction must be a different one from your "Primary Detachment".
>All in all, it looks as though Combined Arms Detachment, and Allied Detachment are the -only- detachments so far...but that there will be others...and they will have their own, unique, FOCs. They will also have their own requirements and Command Benefits. Some Detachments, for instance, may have the requirement of needing to consist of units taken solely from the Orks Faction...
>Formations, consequently, are also Detachments, but of a very special kind. Formations, consequently, are the -only- kind of Detachment that an Unbound army may take.
>Lastly, with regards to Factions, is that each Codex Supplement is specifically the -same- Faction as the Codex that it is a Supplement for. Codex: Clan Raukan -is- the same Faction as the Space Marines Faction. Codex: Iyanden is the same Faction as the Eldar Faction. So yeah, you can't have an Allied Detachment of Crimson Slaughter to your Primary Detachment of Chaos Space Marines...but you really don't need to...you can take a Crimson Slaughter Combined Arms Detachment instead.
