What is the difference between miracles, signs, and clear proofs?

The clear signs mentioned in the words of Allah Almighty: "And We certainly gave Moses nine clear signs," have been interpreted by scholars as miracles, such as the staff, the hand, blood, the flood, locusts, lice, frogs, and the parting of the sea. It may also refer to the verses of the revealed scripture, or the cosmic signs indicating the Oneness of Allah. A miracle is an extraordinary event, whether a saying or an action, that defies normal custom, when it aligns with the claim of prophethood, accompanies it, and corresponds to it in the form of a challenge from the outset, such that no one else is capable of it. The signs and proofs indicating the prophethood of our Prophet Muhammad, peace and blessings be upon him, are numerous and diverse, and they are more abundant and greater than the signs of other prophets. These terms are called 'proofs of prophethood' and 'marks of prophethood.' The terms 'sign' (ayah), 'clear proof' (bayyinah), and 'evidence' (burhan) are more indicative of the intended meaning than the term 'miracles' (mu'jizat), because the word 'mu'jizat' (miracles) is not found in the Qur'an and Sunnah (definition).