Beethoven's Piano Sonata No. 14 is also called the Moonlight Sonata. The first movement is smooth, like the moonlight in a quiet and clear night; the second movement is vivid, just similar to the moonlight in a night with few clouds and gentle breezes; The last movement, in contrast, is quite strong and violent, it is more like thunders in a stormy night, rather than moonlight.
So I'm a bit confused.
Is the 3rd movement really a component of the Moonlight Sonata?
Why it is so strong?