A correlation is exactly what it sounds like: a co-relation, or relationship — like the correlation between early birds waking up and the sun rising. But corollary is more like a consequence, like the corollary of the rooster crowing because you smacked it in the beak. Both words love the math lab but can hang with the rest of us, too.

A correlation is a relationship, but not a cause and effect one. In statistics, a correlation is some connection between random variables or data values. Since correlation is a kind of relation, it's often followed by "between." Here are some examples of correlations out in the world:

Correlation is not necessarily causation, so I'm sure this has nothing to do with the departure of Rahm Emanuel. (New York Times)

Their study looked only at wider geographical patterns, showing a correlation between an area's radon levels and rates of the skin cancer. (Reuters)

Corollary, on the other hand, is one thing naturally following another. In mathematics, a theorem is a statement proven true through reasoning. Its corollary is a statement so closely related that it doesn't need to be proven independently. For the rest of us, it's more like the aftermath of something. Let's look at some examples:

The corollary to this finding is that dairy products have no effect on cough, he said. (New York Times)

There is a natural foreign policy corollary: those who see America as a work in progress are less likely to view it as exceptional. (Time)

How can non-math geniuses keep the two straight? Remember that correlation has an equal, though not necessarily defined, relationship. Corollary is more like a consequence.