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Minnesotan here. Dinner is the evening meal to us, with supper being an old, outdated term for dinner.
When we say we're having Christmas dinner, we literally mean the evening meal. We're too busy opening presents and hanging out with family to have a big lunch; we usually just snack through lunch. Maybe put out a meat-and-cheese plate for everyone, maybe make some sandwiches.
In the evening, that's when we prepare a feast for everyone. That way, we've had a whole day to mingle and enjoy company and we're not immediately jumping into preparations for a giant meal.
My wife is from Nebraska though, and she calls the midday meal dinner. She's been having trouble adjusting to Minnesotan customs.
Former Minnesotan here. Growing up, dinner was the large meal, supper was the evening meal if the large meal had already been eaten.
A common example would be a Sunday pot-luck dinner after the church service, and a little supper around 6 that evening.