Today was a nice spring day here in Germany so I played a bit with my spectrograph. One minute there was full sunlight - the other minute the sun was hidden by nice white clouds. I took the two spectra to compare them. (Sorry, no calibration yet. I don't have a fluorescent lamp here at the moment.)
At first glance the two intensity curves are pretty similar. At least the overall appearance of the outline of the curves looks pretty much alike.
But if you look closer, you will see that the direct sunlight curve starts "earlier" (further into the blue/violet range) and ends "later" (further red). Some parts of the sunlight get swallowed by the clouds. There are certain intensity dips that are easier to see in the photos than in the curves. In diffuse sunlight a lot of yellow is missing, part of the turquois and violet. Some wavelengths (most of the green and blue) get through okay though.
In future, if I ever manage to calibrate the curves, I will theoretically be able to say what molecules cause which "curve dip" though my first guess would be that most of it will be due to water molecules...