I don't really see how you could take either of those to mean anything except the loss of hit points means that bodily harm is being received.
What bodily harm is caused by imagining you're falling into an (illusory) pit? Or by having your ego whipped by a psionic attack?
I mean an Ogre is walking along, the illusionist casts phantasmal force creating the illusion of a pit, the Ogre (being dimwitted) imagines that it has fallen into the pit. Are you saying its legs break? What broke them?
Yes, since as you noted, he's being hit by arrows, so of course he's taking damage, i.e. being wounded.
So you really do envision that fighter as having all these arrows sticking out of their body, as they fight on unhampered?
And yet he flat-out says that they're resulting in damage being taken, to the point of spelling out that means physical wounds.
From the PHB, p 34:
Each character has a varying number of hit points, just as monsters do. These hit points represent how much damage (actual or potential) the character can withstand before being killed. A certain amount of these hit points represent the actual physical punishment which can be sustained. The remainder, a significant portion of hit points at higher levels, stands for skill, luck, and/or magical factors. . . . the majority of hit points are symbolic of combat skill, luck (bestowed by supernatural powers), and magical forces. . . .
Rest also restores hit points, for it gives the body a chance to heal itself and regain the stamina or force which adds the skill, luck, and magical hit points.
I don't think
potential damage - ie the threat of damage averted in virtue of skill, luck and magical forces - manifests as physical wounds.
And from the DMG, pp 61, 81, 111-12:
As has been detailed, hit points are not actually a measure of physical damage, by and large, as far as characters (and some other creatures as well) are concerned. Therefore, the location of hits and the type of damage caused are not germane to them. While this is not true with respect to most monsters, it is neither necessary nor particularly useful. . . . Damage scored to characters or certain monsters is actually not substantially physical - a mere nick or scratch until the last handful of hit points are considered - it is a matter of wearing away the endurance, the luck, the magical protections. With respect to most monsters such damage is, in fact, more physically substantial although as with adjustments in armor class rating for speed and agility, there are also similar additions in hit points. . . .
It is quite unreasonable to assume that as a character gains levels of ability in his or her class that a corresponding gain in actual ability to sustain physical damage takes place. It is preposterous to state such an assumption, for if we are to assume that a man is killed by a sword thrust which does 4 hit points of damage, we must similarly assume that a hero could, on the average, withstand five such thrusts before being slain! Why then the increase in hit points? Because these reflect both the actual physical ability of the character to withstand damage - as indicated by constitution bonuses - and a commensurate increase in such areas as skill in combat and similar life-or-death situations, the "sixth sense" which warns the individual of some otherwise unforeseen events, sheer luck, and the fantastic provisions of magical protections and/or divine protection. . . .
Consider a character who is a 10th level fighter with an 18 constitution. This character would have an average of 5% hit points per die, plus a constitution bonus of 4 hit points, per level, or 95 hit points! Each hit scored upon the character does only a small amount of actual physical harm - the sword thrust that would have run a 1st level fighter through the heart merely grazes the character due to the fighter's exceptional skill, luck, and sixth sense ability which caused movement to avoid the attack at just the right moment. However, having sustained 40 or 50 hit points of damage, our lordly fighter will be covered with a number of nicks, scratches, cuts and bruises. It will require a long period of rest and recuperation to regain the physical and metaphysical peak of 95 hit points. . . .
the accumulation of hit points and the ever-greater abilities and better saving throws of characters represents the aid supplied by supernatural forces.
Mere nicks and scratches, at worst, and
not actually a measure of physical damage.