So how would this work on the off-chance of there being more civs than races on a map? Would there be more variety within a race or would all civs pick the same race-type? Like, would it be possible for a civ of wood-elves to go to war with an entirely different civ of high-elves?
Its a vanilla raw feature. Its like the animal men, if an "underground" civ is placed the game chooses one of the defined races (ig ant man, bat man, whatever man).
They all have equal chances to be chosen. Whether they war or not depends on the ethics (they share everything entity related, like items, reactions and diplomats).
This does change 1 civilisation to a certain races, there will never be multiple races in one civ without Meph sorcery.