"Etude simultanée de deux variables X et Y définies sur une même population P : mettre en évidence une éventuelle liaison (relation, dépendance) entre les variables"
https://fermin.perso.math.cnrs.fr/Files/Chap2.pdf

"Qu'est-ce que la corrélation ?
La corrélation est une mesure statistique qui exprime la notion de liaison linéaire entre deux variables (ce qui veut dire qu'elles évoluent ensemble à une vitesse constante). C'est un outil courant permettant de décrire des relations simples sans s'occuper de la cause et de l'effet."
https://www.jmp.com/fr_fr/statistics-knowledge-portal/what-i...

"Correlation and Dependency. Aren’t They One and the Same?
For those starting out in analytics, it can be quite confusing to understand the underlying difference between the terms ‘Correlation’ and ‘Dependency’. In statistics, when we talk about dependency, we are referring to any statistical relationship between two random variables or two sets of data. Correlation, on the other hand refers to any of a broad class of statistical relationships involving dependence. Let us further define these two terms:

Dependency: A variable whose value depends on the value assigned to another variable (independent variable).
Correlation: The relationship between two or more variables is considered as correlation. The correlation coefficient always assumes linear relationship regardless of whether that assumption is correct or not."
https://u-next.com/blogs/data-science/correlation-and-depend...

So, dependency means that there is some relationship between the variables that you are studying (could be positive, negative linear etc.), whereas correlation assumes that the dependency is linear. Just because a correlation test does not give a good result does not mean that there is no dependency.
https://helios2.mi.parisdescartes.fr/~obouaziz/Chap5Tests.pd...
https://www.stats.ox.ac.uk/~cucuring/Lecture_2_Correlations_...