Difference between the terms abnormal behavior and mental illness?

Is there a meaningful difference between the terms ; abnormal behavior and “mental illness”? Why or why not?

Abnormal behavior, as it relates to psychological disorders, would be “ongoing” and a cause of “significant distress”. A mental disorder describes a patient who has a medical condition whereby the medical practitioner makes a judgment that the patient is exhibiting abnormal behavior based on the DSM-5 criteria.

What do you think about the significance of the general public’s perception (and corresponding social stigma) about such problems when referring to them as diseases vs. purely “mental” problems that are “just in your head”?