Does meekness and humility mean the same thing?

No, they do not. To be "meek" is to be extraordinarily patient. Those who are meek understand that "good things come to those who wait" and that it is in the nature of things that the good and worthy outcome often takes far longer to come about/happen than less worthy outcomes.

To be humble, on the other hand, is to be modest; to not be proud or arrogant, or to think that one is better than, or superior, to others.

It is usually only those who are humble who have the strength of character to also be meek -- but they are not the same state of being.