Yeah, I think there is more to it, but it stems to how thin something is.
Like, if your body had a durability of 20 joules per square centimeter and you took a punch of 100 joules, it should destroy you right? But the punch's size makes the energy spread to 10 square centimeters, aka each cm^2 receives only 10 joules, so your durability tanks it.
But, if a paper hits you on 1 millimeter squared, and causes 1 joule, it will cut because if 1 cm^2 tanks 20 joules, 1 mm^2 would only tank 0.02 joules.
This is all only on real life though, in fiction they tend to either be normal damage, durability negation because plot or strong dudes have dense skin.
Whoever, we tend to considered stuff with piercing damage as an AP advantage over comparable opponents, as long as they are treated as such.