In 1e, when you took a hit, you could immediately determine what it represented in-world on the basis of the damage taken vs. the character's remaining hit points. Because you knew how long it would take to heal that wound, and how much it affected the character, you could peg it really, really closely. You were, in effect, telling the story as it unfolded.
However, in 4e, when you take hit point damage, you cannot immediately tell what that damage represents in-world.
I don't understand why you say this.
In 4E, you can recover from any blow that doesn't kill you outright unaided with 5 minutes' rest, assuming you have enough healing surges. This means that over the course of combat any damage you take cannot reflect injuries that would take more than 5 minutes' rest to heal.
This is why I say that when your hit points go negative, you pass out from the sudden shock rather than because you've been too badly damaged to remain fundamentally conscious. Healing surges reflect your ability to shake off shock and recenter yourself - when they run out, it's not that you're hurt any worse off than you were before, it's that you've tapped out your ability to recover from that shock, but with a good rest you're refreshed.
Could there be ways to regain that ability other than rest? Yes, though many of them that you could think of are not explicitly allowed. You could drink from a stream and be refreshed enough to regain 2 healing surges. Why? Well, you can decide that. Perhaps your character is part merfolk, perhaps the stream flows from the fountains of the Bright City, perhaps it has been infused with vital energy. The default setting assumes that such springs do not exist, so if one does it would be because of DM fiat. But if a DM is planning an extended dungeon dive then scattering such springs through would be a means of giving the characters the ability to recover without having to worry about where they stop to rest for 6 hours.
At least one way is spelled out. When a deadly trickster pulls off his epic trick he regains all hit points and healing surges. So whatever the epic trick includes, it must also completely refreshes him as though he has rested. Perhaps he points the other way and, while Time is distracted, picks its pockets of 24 hours for himself.
But somewhere in the point between fighting fit and unconscious, you do become obviously wounded - when you pass from about 50% hit points to 50% or below, and become bloodied. Here are the characteristics of the wound you have suffered when you are bloodied: it does not slow you down; it does not weaken your attacks or make them less inaccurate; it does not on its own reduce your hit points any further; it does expose you to certain kinds of environmental damage and effects that a non-bloodied person would not be exposed to; it does signal to enemies, allies, and casual observers that you are wounded; it does signal to yourself that you are wounded; and if you take the few seconds to use your second wind you can tend to it so that you are no longer wounded.
What is the second wind? It's a single moment of clarity that you can seize on to refocus and recover, just as if you were resting after the fight was over. Why can't you use it more than once per combat? Combats are fast and confusing and you can only muster that concentration once, barring special effects such as divine intervention. Try to grab it again and it won't work. It also won't work if you've been battered around so much during the day that all your ability to recover is gone.
If it's important for you to describe damage to your character, you can now imagine many "bloodied-type" wounds your character could suffer, depending on the source of damage, element of damage, and possibly location on the body. As you take damage in combat, think about these wounds. The strike that puts you into bloodied status could inflict one of them, but so could any single strike you take before then - the wound won't just become obvious until you drop to 50% hit points. (This is for cases where you have 50 hit points, a dragon bites you for 24, and then its kobold cutter minion dings you for 3. It is fine to say that the obvious wound came from the dragon bite and you were suppressing it with force of will until the minion rattled you and broke your concentration.)
Why is it okay to think about such things beforehand? Because describing damage to your character is satisfying for you, or because it will be one element in a story that you are enjoying telling with the other people at the gaming table. It gives them something real to bounce a hook off of - they can tend to that wound with first aid or have somewhere to lay on hands. But considering the game as writen, there is no other reason. There is nothing in the mechanics of the game to suggest that it matters what sort of wound it is that bloodied you. So, you are free to decide it for yourself, to your own satisfaction.