Correlation and causality are ways to describe the relationship between two events. If two events are correlated, then they usually occur together. For instance, people with 40 or more CAG repeats usually develop HD. People with 35 or fewer repeat numbers usually do not develop HD. These instances are examples of correlated events. Correlation also implies that two events change in a systematic way. For example, a negative correlation between two things implies that as one increases the other usually decreases. Hence, as the number of CAG repeats increases, the age of onset decreases. In contrast, a positive correlation between two things implies that as one increases the other increases as well. The age and height of children are positively correlated. Hence, older children are usually taller than younger children.
On the other hand, causality describes the cause and effect relationship between two events. The observation that two events are correlated is not enough to conclude that one causes the other to happen, nor is it enough to conclude that one doesn't cause the other to happen. In other words, correlation does not imply anything about causality. Correlation shows that two events are related, but it does not determine their cause and effect relationship.
For example, many psychological studies have shown that children who watch violent television shows are more likely to exhibit violent behavior. The general trend shows that a child's "level" of violence is positively correlated to the amount of violent television programs a child has seen. That is, the more violent TV shows a child watches, the more violent behavior he or she is likely to exhibit. This information does not prove that watching the television shows actually causes the children to become violent.
In this example the two events, viewing violent television and exhibiting violent behavior, are correlated. Hence, if a child is violent, it is very likely that he or she has also watched violent television. However, the violent television itself is not necessarily what caused the violent behavior. The child could exhibit violent behavior for any number of reasons. For example, it is possible that children who behave violently for other reasons are especially fond of watching violent television. The correlation between the two events is just not enough information to conclude anything about cause and effect. Thus, violent behavior is correlated to viewing violent television, but not necessarily caused by it.
In the case of HD, we know that the number of CAG repeats is negatively correlated to the age of onset. Usually, people with more repeats have an earlier age of onset. The important point to remember is that we do not know whether the additional CAG repeats are the actual cause of the earlier appearance of symptoms.