Oh yes I got my definition of correlation slightly wrong. Correlation doesn't necessarily mean that two things have the same cause but they do relate in some way either by having a common cause or by occuring in the same system. They definitely have more in common than happening just at the same time or right after each other like a coincidence.

I didn't claim that correlation equals causation and I hope you didn't get the impression because this would be oviously wrong.

Edit: I stand corrected and today I learned that "correlation" means that two things have a statistical relation without any causal relation implied. There can be a causal relation but it's not necessary. The key takeaway for me is that correlation describes a statistical relationship.