I don't think they represent injury, and I'm not being disingenuous.
Generally I think the loss of hit points consists in being set back in the current fight, but what that being set back looks like I think is very contextual. Some instances of hit point loss correspond to the suffering of an injury. Some don't.
Suppose a PC starts the day with 20 hp, and then in a fight with Orcs is hit 4 times, taking average damage from their swords, and thus loses 18 hp. The PC now has 2 hp left, and is likely to be felled by any Orc blow that they cannot dodge or parry. The player knows this. I don't see how the PC knows it - especially if the combat in which they lost 18 hp is over, and they've caught their breath and bandaged any nicks and scratches. They might know that they're not at their peak; but I don't think they can know that the next Orc blow will probably be fatal (or near-fatal, depending on edition).