Both humiliate and shame are verbs which mean the same thing which is "to make someone feel ashamed", however, shame can also be seen as a noun to mean "a painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behavior."

humiliate = Do not humiliate me because you do not know whats happened. Shame = I feel shame that she is asking people for money. ( I feel bad and unpleasantness) the best to understand both, to read more context include these words