So, what you're saying, is that those of us who have a "hit" and "damage" follow the actual dictionary definitions of the real words are playing D&D wrong? Because that's complete and utter BS.
I wouldn't say that you're playing D&D incorrectly. I would say that, while you're using the dictionary definition of "hit," so are we.
Hit | Define Hit at Dictionary.com
7. to have a marked effect or influence on; affect severely.
10. to reach or attain (a specified level or amount).
Damage | Define Damage at Dictionary.com
1. injury or harm impairing the function or condition of a person or thing
So, when I hit someone, I have hit (reached or attained (via the die roll)) their AC. I have also hit them in that I have a marked effect on them (by reducing their hit points).
Damage to the hit point pool impairs its function; there is less of it to account for the next hit, and the one after that.
Now, a hit can certainly be an actual physical hit. I doubt many people here have said that it's not (though I'm sure some have). But it need not be. And, unless it puts someone into the ground, it's not a blow that can't be healed naturally or via magic.
The trick is not to narrate yourself into a corner. If you have no magical healing, then don't describe a vicious assault that skewers your fighters gut, pulling out his intestines when the spear is removed. No one is going to survive that kind of wound without magical help. Even if the damage could be repaired, the chance of infection is too high. If your healer is, for example, a warlord, perhaps a solid critical hit slams into your shield hard enough to make it feel as if your arm has broken. Or maybe an arrow pierces the thigh muscle, but goes through cleanly, easily disinfected and wrapped; it will be painful to continue, but the person can continue. Or maybe that orc's axe hits hard enough to crease the fighter's plate, causing a bruise, and maybe a rib fracture--painful, but possible to work through if wrapped, especially with a high pain tolerance.
Narrate the combat to the capabilites of the group. That's the idea here.