The definition falls short because what is deemed selfish or not, is relative to society's evaluation of it, an evaluation which is in itself, based on selfishness. Selflessness is relative to how much you can benefit others, and how much you can avoid benefiting yourself. Which is impossible (or not but thats a tangent). Society deems egoists those who benefit themselves MATERIALLY. But materialism isn't the only way through which someone could be selfish. Everything we do is 100% towards our own well-being, including altruism or martyrdom. The instances in which we cooperate or do good to others are just our motives intersecting with other's, one in which a moral consensus is met between an individual and society.
Someone might believe that they are selfless, but that's their own mind creating illusions and disguises. Which is something that the mind LOVES doing and does with ease .
Your mind evaluates your desires and decides which one is more useful for the integrity of the mind-system as a whole. For example, a starving man gives his food to someone else because his sense of integrity and honor are much greater (in the present) than the need of bodily self-preservation. Which is really not any different than the man stealing food to eat. Its the same type of selfishness applied through different means. ( I know that's not what you meant though. When one does something accidentally, their motives aren't really implicated in their actions. Their actions could maybe have some weight, but that would be purely coincidental. )
The man who decides to starve out of honor, all while ensuring the well-being of others, might eventually lose all his principles when a greater need is met (for example, one's life, which surprisingly isnt the greatest thing for man). A pacifist might even kill someone to not starve. Or their desire for pacifism/self-integrity/idealism might be so great that they would sacrifice their life for ideals, interestingly out of self-preservation. The soldier who jumps on a grenade to save his comrades does it because his ideals are much greater than his own life. Or he does it in fear of having to continue living after having bend his own life philosophy. Or the regret he might experience as a result of not having sacrificed himself. Or even not understanding what death truly is (we don't), meaning that the mind cannot properly evaluate and assess the imminent threat of death. IIn this case, the soldier who sacrifices himself does it entirely for his own well-being. He is deemed selfless because his motives intersected with other's, he saved others while giving away his own life! And because society's perception of egoism is so rudimentary that as long as you don't benefit yourself in a material, physical way, you aren't an egoist.
Selfishness is objective. Its one and one thing only. Its experienced and described differently by everyone, but that doesn't change at all what selfishness actually is. People ALWAYS objectively follow their own well-being. We are intrinsically selfish. Some individuals might believe with absolute certainty that they aren't, but thats just the mind creating disguises and illusions