Association

Association is the broad idea and correlation is one narrow measure of it. For two quantitative variables you describe an association by its form (linear or non-linear), direction (positive or negative), strength, and unusual features, so a curved pattern still counts as a real association. For example, braking distance grows roughly with the square of speed, so 20, 40, and 60 mph pair with about 20, 80, and 180 feet: doubling the speed quadruples the distance ($4 \times 20 = 80$), a strong association that no straight line captures well. Association also applies to two categorical variables, where you compare conditional percentages in a two-way table and correlation does not apply at all.