It absolutely can be both. You high stick me.
That's a penalty called high sticking.
I overreact to the high stick and exaggerate it's effects.
That's a penalty called embellishment.
Where is the problem?
So what player was harmed/impeded/fouled/etc by the reaction to the painful stick to the head? Is the expectation this and to just keep your eye on the stick into your face?
No one is in the position to judge the severity of a reaction. Even so, what makes that reaction's impact to the game = to original penalty? At worst, it could be a 1min.
If I hit my stick off your shoulder and then you throw your head back faking a high stick, then you ALONE should go to the box. This PK risk is enough to get the desired effect from the game. What is the risk in embellishing everything if the worst that can happen is 5v5 and we both go? You are still going to fool enough dumb refs with great acting. If you earn an embellishment PK for your team, coachy-no-likey, you ride benchy.
Embellishment rule is dumb because it is unequal and doesn't really police what it was intended to do.