The famous sentence is that correlation isn't causation, the inverse is always true. Correlation means that two things tend to increase and decrease together or inverted, that they both have a relation with whatever else. Causation means that one thing is the cause of another thing, meaning that one or several things increasing or decreasing are the sole cause of another thing hapenning.

By definition, causation implies correlation, but the inverse isn't true.

Small example: months where more icecream is eaten have an increased average of tanned people, on average. Does this mean that eating icecream gets you tanned? Nope, it means that on summer people eat more icecream (partial causation) and on summer people go more to the beach and get tanned, again, being summer isn't the causation of getting tanned, it's just a correlation because it's sunnier. As we know, being in the sun is the causation of getting tanned.

In any case, either you mixed the two terms or you got confused, I hpe this clarified it :]

By definition you can't have causation without a correlation, but the two aren't the same. It does feel like your original intent was 'correlation doesn't equal causation' though.