Psychiatrists are medical doctors trained to understand mind-body interactions who are typically also trained in certain talk therapies. Therapists are primarily trained in talk therapies and can have backgrounds in psychology, social work, or other fields. Psychiatrists are licensed to prescribe medications to treat mental health conditions, while the other types of therapists are not.
That distinction means that you should find a psychiatrist when suffering from severe depression, hallucinations, or psychotic episodes, particularly when these symptoms interfere with your daily functioning. The mental health issues mentioned above are among the most severe, and treatments with medication are often quite effective.
Talk therapy alone does not successfully treat these issues.
Some forms of ADHD respond well to medicine, and others do not. People who experience the latter often receive help via talk therapy in the form of coping skills to deal with the specific effects of ADHD. Talking therapy is also the primary tool used for those dealing with relationship issues, emotional trauma, or seeking to gain self-insight. Medication might help deal with the anxiety or other challenges that surround those issues, but the problems themselves do not respond to medication. Instead, they require changing how individuals think about or behave in response to specific situations or people who play a part in their lives.