There's also an important distinction in terms of how fighter wings stay on the field: a fighter wing only remains in the battle as long as it has at least one fighter in existence - including fighters currently being built on a carrier.
An example is probably needed. Suppose you're running two wings of talons backed by a single flight deck. One wing of talons flies too close to an enemy cruiser and gets obliterated; now you've got one wing of talons still flying around, and one wing that's still "in combat" because it's being regenerated by that flight deck. However, if the second wing is destroyed at this point, it's out of the battle - it has nowhere to go, and is out of the fight. (You won't lose it after the battle, though, unless the enemy killed all of your carriers as well.)
As an addendum, some mods include fighter wings with only a single fighter in them; these can never be regenerated at a carrier, because when that one fighter blows up, there's nothing already being built, and so it's removed from the field.
How many flight decks you "need" per wing of fighters you're using is somewhat debatable. As I don't use fighters much, I have no particular recommendations here, beyond "one flight deck per wing of fighters is probably overkill".