Correlation does not imply causation but it does imply having something to do with the other. Your first sentence contradicts itself.
Correlation does not imply having something to do with another.
For example, in the first decade of the 21st century, spending on space exploration had a 99.8% correlation with a specific subset of suicides (hanging?).
By its very definition, "correlation" means exactly "a mutual relation": https://www.dictionary.com/browse/correlation The example you're giving is called coincidence not correlation. There are times where words' etymologies loose their connection with their current meaning, but that is not the case here, where we have "con" meaning "together" + "relation", which is a logical construction agreeing with word's meaning.
> Statistics. the degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together.