Maybe little. Traditionally "clinical depression" is what we call major depression and was thought to be what was responsive to medication as the person's depression doesn't change with the environment eg would still be depressed if won the lottery. But medications help even some reactive depressions since some people over react to situations. This is common in atypical depression. See my book on amazon. Com.
Causation. Reactive depression has a specific cause, i.e. The loss of a loved one, or a job, difficulties in social relationships. Clinical depression is usually some chemical imbalance in the body, often genetically transmitted. Since our culture is uncomfortable with negative emotions, we often rush to "help" people who seem depressed, often with meds. Check your reality, seek appropriate help.
Imperfect terms. Both are imperfect terms, but to me "clinical depression' implies that a person meets diagnostic criteria of a depressive mood episode, while 'reactive depression' implies a clinician's opinion that a person's depression might be the result of external stress. Officially, psychiatry does not make this distinction.
Not a diagnosis. Clinical depression is not a formal diagnosis, it just means depression (whatever the cause) is severe enough to warrant treatment. "reactive" depression is a reaction to a specific event-- a loss, a specific life setback or stress-- in someone who had not previously been experiencing depression.