From my perspective, a concession is bowing out of the fight when you could keep going. So, you can concede before the dice are rolled, and that's usually pretty easy.
After the dice are rolled, well, you can still look at the result and say something like "This conflict isn't worth fate points or a moderate consequence; what's the take-out result they were aiming for?"* and then maybe negotiate a bit to get a concession - but this sort of thing is more likely to result in a concession of "beaten up and left for dead, with a moderate consequence of 'bruises all over'," or maybe "Not only do I not get the information I wanted from this guy, but I'll also take a temporary aspect of 'Dr. Morrison is clearly innocent', which he can call in later for help or protection."
And what if, in order to stay in the fight, the PC would have had to spend an extreme consequence? Well, you can still - by my definition - technically concede at that point, but doing so is probably going to either involve an aspect change or be nearly indistinguishable from a take-out result, or possibly both.
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* Another example I've seen on this boards was someone who said "You know, I think it might be interesting to get taken out here." - I think the context was a soulgaze or using the Sight on a draconic scion. From my point of view, that's a very clear concession; the player could easily have taken the mental hit, but chose not to.