Modest does not mean poor, but humble does.
Modest describes the personality trait of not flaunting oneself, talking oneself up or putting oneself on display. Modest behavior can be a response to compliments, praise or follow an achievement. Modesty can also manifested physically (for example, "dressing modestly", "modest accessories", "modest smile").
A humble person accepts someone else's superiority and does not challenge them and try to be superior. They have humility.
In summary, being modest refers to your behavior, being humble refers to your ego.