What is the difference between Ahadith Qudsi and the Qur'an?

Aren't they both from Allah, revealed to the Prophet (saw)? I was in Tajweed class yesterday, and the teacher was saying how professors in some unis like Columbia and Harvard use this to attack Muslims. They'll ask them what a Hadith Qudsi is, and then when they hear what they want, they'll trap the... show more Aren't they both from Allah, revealed to the Prophet (saw)? I was in Tajweed class yesterday, and the teacher was saying how professors in some unis like Columbia and Harvard use this to attack Muslims. They'll ask them what a Hadith Qudsi is, and then when they hear what they want, they'll trap the students by asking them what the difference between Hadith Qudsi and Quran is.

I think I'm missing something here, there has to be a difference, what is it?
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