All fun isn't it
This has been mentioned on a few other topics but still is unclear.
In the case of something like space marines (ravenguard) having a unit of space marines (salamanders) for instance the FAQ sorted it out by saying they are allies, so require an allies matrix to use as they have different chapter tactics.
Some started to argue that you could take a Primary for a Space Wolf army as a Combined Arms as Imperial Guard. This seemed to get quoshed though with the FAQ for Space Marines that said that a space marine chapter would need to take an allied detachment if it wanted to include space marines with different chapter tactics. As this proved that "Armies of the Imperium" need to ally with each other rather than combined arms.
The only arguing point at the moment seems to be with CSM - CSM CS - CSM BL. The supplements say that CS and BL are able to ally to CSM, but the new rule book says that they all class as the same 'Faction'.
With this the use of the word 'Faction' seemed to be used in 2 separate context. One to refer to the army (aka Space Wolves, Grey Knights, CSM, Tyranids), but also refers to it in the collective group (Armies of the Imperium).
I think what was meant by the bit saying supplements are counted as the same faction as the core book was only meant to refer that for the purpose of the allies matrix they count as the core book. So Black Legion or Crimson Slaughter count as Chaos Space Marines (various) for the purpose of being able to ally with Chaos Daemons or whatever. NOT that if you have a Black Legion army you could have it as your primary detachment but then include a Crimson Slaughter Combined Arms and a Chaos Space Marine Combined Arms (taking advantage of the additional daemon weapons and stuff). BUT you could still use allies formations to get them.
What you cant do however is have a Crimson Slaughter Primary Detachment you could not if have a Crimson Slaughter allied detachment if you only wanted 0-4 elite/fast/heavy, but only wanted 2-3 HQ total and 3 Troops.
The same I guess would be true of Tau / Farsight though I don't know if in the supplement for them if it says you can ally Farsight with Tau. I know in the case of Iyanden that it does not give them the option to ally with Eldar, though that is most likely because there is no point. The Iyanden army gets a few special extra rules, BUT has no negative things, and can still use the Codex Eldar : Remnants of Glory (though not combined on the same character who uses the Iyanden : Gifts of Asuryan).