What key difference do experiments have that correlation studies do not have?
Experiments actively change independent variables. Correlation studies do not. For this reason, experiments are more likely to prove causation.
The key difference between an experiment and a correlation study is that in an experiment, the experimenter ACTIVELY CHANGES the independent variable(s) of study, tries to control or randomize other independent variables, and measures the effect on the response. In a correlation study the analyst PASSIVELY RECORDS the state of independent variable(s) and response(s).
In Box, Hunter, and Hunter's book "Statistics for Experimenters" the authors show an intriguing plot of the human population in Oldenburg on the y-axis versus the stork population on the x-axis during the years from 1930-1936.
The plot shows that as the stork population increases, the human population is increasing. A misguided person might reach the conclusion that the storks are CAUSING the human population to increase (perhaps the storks are BRINGING the babies!) However, we know this is not the case. Instead, what may be happening, is that as there are more humans, there are more rooftops for storks to roost.
If you truly believed that the storks were causing the human population to increase, then your experiment might be to take out your rifle and start shooting storks to see if the human population decreases as well. Because we understand this system, however, we predict that it is highly unlikely that shooting storks will have any effect on the human population (unless the shooter is Vice President Cheney).
This demonstrates that while this correlation study shows correlation, it does not help us understand causation because no independent variables were actively changed by the people conducting the study. They simply recorded data. They did not run any experiments.