What is the difference between karamat (divine graces/miracles bestowed upon saints) and mu'jizat (miracles performed by prophets), and was what Al-Khidr did a karamah or a mu'jizah?

A miracle is a proof of prophethood, and it is an extraordinary event. As for karamah (divine favor), it is for the saints and is not a challenge. Al-Khidr (peace be upon him) is a prophet according to the majority of scholars, and Allah informed him of the unseen through revelation. What Al-Khidr did was by Allah's command through revelation, and it was not a karamah. This indicates his prophethood.