Humility vs Modesty
Modesty is pretentious; the apparent lack of concern is just a facade that betrays tremendous concern for the opinions of others.
"Modesty is the gentle art of enhancing your charm by pretending not to be aware of it." -- Oliver Herford
Modesty consists of deliberately belittling one's own ability and accomplishments for the opportunity of receiving praise from others.
Humility, is acknowledging your intrinsic self-worth while not drawing unnecessary attention to yourself. You're humble; you neither eulogize your virtues, nor do you make yourself out to be worthless. It does not mean refusing to recognize your strengths, talents, and skills. It means that while you declare your strengths, you also acknowledge your weaknesses.
Humility means being authentic, while acting modest implies being inauthentic. It is no accident, then, that we use the verb "act" when we talk about modesty.
"Perfect humility dispenses with modesty." -- C. S. Lewis