[mattkrause]

That matches my experience too.

Correlation, in general, just means some sort of statistical dependence: knowing x tells you something about y. It's often "operationalized" by computing Pearson's r: it's easy to do and there's lots of associated theory.

However, I would find it absolutely bizarre if someone showed a plot with obvious non-linear dependence and described it as "uncorrelated". In that case, the low r reflects a failure of the measuring tool rather than something being measured.