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Correlation vs causation. Good question. Tha answer is a bit long but I'll try a short synposis.

Correlation (as I was using the term) is a statistical measure of relationship. (The formulas are in any elementary statistics book and are available on the net.) For example, one might measure the heights of parents and the heights of their offspring. A plot of parent-height vs offsprint-height will show a tendency for tall parents to have tall offspring and short parents to have short offspring. (Note that the relationship isn't perfect, short parents can have tall offspring, and vice versa.) There is a measure called the correlation coefficient which can be either positive or negative depending on what is being measured; it's actually the cosine of the angle between the (normalised) data vectors. The square of the correlation coefficient gives a estimate of the "strength" of the correlation. All this is statistical in nature and depends on sample size, etc. Anyway, things with high correlation strength are often causally related.

Causation is a scientific (or physical or chemical, etc. rather just statistical) relationship. For example, setting something on fire causes it to burn or having the gene for Huntington's Corea actually causes the disease. Causation is stronger (epistemologically) than correlation but neither really implies the other logically. It is possible to have random causes where the correlation coefficient between "cause" and "effect" (before and after states) is zero.

In the case of race; having certain genes for skin color may be correlated with "race" but all "races" have people with these genes; on the other hand, Huntington's Corea is caused by the gene; those with the gene get Huntington's.

In scientific inquiry, high correlation is a sign that something "interesting" may be occuring. (Of course, if there were no correlation between things that we thought out to be correlated, that would be of interest too.) One can also get "spurious" correlation due to what's called confounding factors. For example, there is a very strong correlation between the consumption of Hershy bars an the number of heart attacks in the US; Both are "caused" by the increase in population. Similarly, the number of babies born is correlated with the number of storks nesting on chimneys for the same reason. This type of confounding makes it problematical to study things like murders, murder rates, gun ownership, etc.

As an example of the use of correlation, in the 1950s some British scientists were trying to find out the reason for an increasing rate of lung cancer. They actually hypothesized that lung cancer was primarly caused by automobile exhaust (or in their case, lorry exhaust.) What they did is look at the correlations between people with lung cancer and exposure to exhaust, smoking, eating habits, etc. (They compared against lots of items; I can't remember their names either.) The only correlation of significance was with smoking; it was much bigger than they expected. Later others have elucidated the mechanism whereby smoke damages lung tissue.