Both would be understood. But, if you want to know the REAL difference, it is this: Above = represents something at a place HIGHER THAN another person or object. Over = represents something that is directly upwards of another person or object. Technically, in your example, "The plane is flying ABOVE the clouds" would be the correct sentence. However, both would be understood and most natives would not know about this technicality.

Either is right, but I would most often say something like "The plane is flying over the countryside" and "The plane is flying above the clouds." It just depends on what you want to bring attention to - is it that the plane traveling across something, covering distance (in this case use over) or do you want people to think about the fact that the plane is so high, you can look down on the clouds (in this case use above).

Both are correct Victor. "The plane is flying above the clouds" - location: above the clouds. The plane is flying over the clouds - direction/movement. It is in the process of flying, over /across/ past the clouds.