It’s a matter of usage. Dinner, by definition, is the chief meal of the day, eaten at the noon hour or in the evening. Supper is an evening meal, especially when dinner is taken at midday.
In my part of the South we eat breakfast, dinner and supper because our main meal has traditionally been at noon. Even if we eat our main meal in the evening, we still refer to the noon meal as dinner and the evening meal as supper. In many other parts of the US, people eat breakfast, lunch and dinner because their noon meal is light and their main meal is in the evening. I think "supper" used to used more frequently but only certain areas seem to retain the use today. My non-southern girlfriend always confuses me when she refers to the evening meal as "dinner.".