Causation implies Correlation, right?
Your observation is correct, however this is not always the case. Simply, there are examples when two variables are correlated, none of the two may be the cause for the other or vice versa.
For instance, it could be a third factor that is the cause for both, and they can appear to be correlated. However, none of the two is the cause for the other one.
For exampe, think of the following line:
"when ice creams sales increase, the amount of drowning deaths increases.
Then, it would be wrong to conclude that increased ice cream sales cause drowning deaths, or vice versa. Both phenomena happen in the summer, though, and it is high temperatures that lead to them.
Alternatively, think of the following.
If you say: "When there's more wind, the windmills are observed to rotate faster."
The wind is the cause (causation), and hence, we have correlation between wind and windmills rotation speed (correlation).
However, if you say it like this: "The faster windmills are observed to rotate, the more wind is observed to be."
From that statement on its own, it is not clear whether windmills rotation causes the wind, whether it is vice-versa, or whether there's a third factor that causes both phenomena to happen.
So, the second statement isn't always true. However, causation implies correlation, yes.
Hope this helps.