What is the difference between correlation and causation, and how would you establish causation?

Correlation means two variables move together. Causation means one produces the change in the other. Correlation is necessary but nowhere near sufficient.

Why correlation appears without causation:

• A confounding variable drives both. Ice cream sales correlate with drownings; temperature causes both. In business, the classic case is that customers who use a feature retain better — because engaged customers both use features and retain, so the feature may cause nothing.
• Reverse causation — the arrow points the other way.
• Selection bias — the way the sample was chosen created the pattern.
• Coincidence, particularly when many variables are tested until something correlates.

How to establish causation:

• A randomised controlled experiment is the gold standard. Random assignment makes the groups equivalent on everything, including factors you did not think of, so a difference in outcome can be attributed to the treatment. This is what A/B testing is.
• Where randomisation is impossible, quasi-experimental methods help: difference-in-differences, regression discontinuity, instrumental variables, or a matched control group. All are weaker and rest on assumptions that must be stated.

Note: The practically valuable habit is asking "what else could explain this?" before presenting a causal claim — and being explicit when you are reporting an association rather than a cause, because stakeholders will act on it as a cause unless you say otherwise.