Correlation is about two variables existing contiguously in time. One may give rise to another.
Causation is about one variable giving rise to another. Causation is not assumed without further endorsement:
In law:
The but for test inquires ‘But for the defendant’s act, would the harm have occurred?’ A shoots and wounds B. We ask ‘But for A’s act, would B have been wounded?’ The answer is ‘No.’ So we conclude that A caused the harm to B. The but for test is a test of necessity. It asks was it ‘necessary’ for the defendant’s act to have occurred for the harm to have occurred. Causation (law) - Wikipedia
In Epidemiology:
A principal aim of epidemiology is to assess the cause of disease. However, since most epidemiological studies are by nature observational rather than experimental, a number of possible explanations for an observed association need to be considered before we can infer a cause-effect relationship exists. That is, the observed association may in fact be due to the effects of one or more of the following:
- Chance (random error)
- Bias (systematic error)
- Confounding
Therefore, an observed statistical association between a risk factor and a disease does not necessarily lead us to infer a causal relationship. Conversely, the absence of an association does not necessarily imply the absence of a causal relationship.
The judgement as to whether an observed statistical association represents a cause-effect relationship between exposure and disease requires inferences far beyond the data from a single study and involves consideration of criteria that include the magnitude of the association, the consistency of findings from other studies and biologic credibility [1].
The Bradford-Hill criteria are widely used in epidemiology as providing a framework against which to assess whether an observed association is likely to be causal.
The Bradford-Hill criteria (J Roy Soc Med 1965:58:295-300)
Strength of the association.
According to Hill, the stronger the association between a risk factor and outcome, the more likely the relationship is to be causal.Consistency of findings.
Have the same findings must be observed among different populations, in different study designs and different times?Specificity of the association.
There must be a one to one relationship between cause and outcome.Temporal sequence of association.
Exposure must precede outcome.Biological gradient.
Change in disease rates should follow from corresponding changes in exposure (dose-response).Biological plausibility.
Presence of a potential biological mechanism. [current scientific framework]Coherence.
Does the relationship agree with the current knowledge of the natural history/biology of the disease? [within current scientific framework]Experiment.
Does the removal of the exposure alter the frequency of the outcome?
https://www.healthknowledge.org.uk/e-learning/epidemiology/practitioners/causation-epidemiology-association-causation