Causality is the relation between an event (the cause) and a second event (the effect), where the first event is understood to be responsible for the second.
In common usage, causality is also the relation between a set of factors (causes) and a phenomenon (the effect).
Anything that affects an effect is a factor of that effect. A direct factor is a factor that affects an effect directly, that is, without any intervening factors. The connection between a cause and an effect in this way can also be referred to as a causal nexus.
‘Correlation does not imply causation’ is a phrase used in statistics to emphasise that a correlation between two variables does not necessarily imply that one causes the other. Many statistical tests calculate correlation between variables.
The counter-assumption, that correlation proves causation, is considered a questionable cause logical fallacy in that two events occurring together are taken to have a cause-and-effect relationship. This fallacy is also known as cum hoc ergo propter hoc, Latin for “with this, therefore because of this”, and “false cause”.
There are many interesting, or shall we say cheesy, examples of spurious correlations.
Here are some more courtesy of tylervigen.