What is the difference between 扰乱 and 捣乱?
扰 in 扰乱 carries the meaning of 'to disturb'; 'to disrupt'

捣 in 捣乱 carries the meaning of 'to smash; to crush'



扰乱(to disturb; to disrupt) is usually in non-physical, non-violent forms
When you talk with your classmate during class, you are disrupting (扰乱) the normal flow of the class
when you look over someone's shoulder while he write, you are disrupting (扰乱) his concentration.

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捣乱 (to create a disturbance) is often in physical, violent forms
When you go smashing up a bar, it is an act of 捣乱 (to create a disturbance)
When you trashing someone's house, it is also an act of 捣乱 (to create a disturbance)

Of course your teacher may consider you and your classmate's disrupting action as 捣乱, in a metaphorically sense.
On the other hand, when the police arrest you for smashing up a bar, you cannot say you are merely disrupting (扰乱) its business. It is more serious than just getting drunk and talked loud.