The game mechanic representation of a concession is a Concession.
I don't agree that they are the same thing exactly - not all the time, no. If one side of a conflict just retreats, and the other side fails to pursue them, effectively ending the conflict, I consider that to be a small-c concession. I'm not going to award Fate points to someone who just leaves the conflict without interference.
There could be any number of reasons for the conflict to end this way, but I imagine the most poignant example would be in a conflict in which the players manage to talk down the opposition. Another would be when the players are on their last few stress boxes, and are perhaps about to offer their own Concession, and the villain, who may only be slightly bruised, decides that the fight isn't worth pursuing. Or realizes he has somewhere else to be. In a case like this, I can see a player being Compelled by an Aspect to keep the up the fight, risky though it may be. The villain may come out on top anyway, or the player, and either way, a Take Out or Concession is probably going to follow.
That said, a capital-C Concession *can* involve the villain leaving in exactly the same way. It can look, narratively, the same. The difference is that someone has to call for a Concession on their own, which begins a negotiation. Consequences are counted, Fate points are handed out, etc.