Quoting [emphasis added] from D.C. Howell's (2012) Statistical Methods for Psychology, chapter 9 (Correlation and Regression), Pg 252:
Although you should not make too much of the distinction between relationships and differences (if treatments have different means, then means are related to treatments), the distinction is useful in terms of the interests of the experimenter and the structure of the experiment. When we are concerned with differences between means, the experiment usually consists of a few quantitative or qualitative levels of the independent variable (e.g., Treatment A and Treatment B) and the experimenter is interested in showing that the dependent variable differs from one treatment to another. When we are concerned with relationships, however, the independent variable (X) usually has many quantitative levels and the experimenter is interested in showing that the dependent variable is some function of the independent variable.
My question is: What is the distinction between a mere difference of the dependent variable (DV) from one one level to another, and the DV as a function of the independent variable (IV)? In other words, the distinction that Howell explains in the quoted text is unclear to me.