from WordWeb:
Supper:
"1.A light evening meal; served in early evening if dinner is at midday or served late in the evening at bedtime"
2.A social gathering where a light evening meal is served"

Dinner:
The main meal of the day served in the evening or at midday
""dinner will be at 8"; "on Sundays they had a large dinner when they returned from church"

So, the most common understanding seems to be that 'dinner' is usually used for the most important meal, or for 'special' meals. Some days, we neved HAD 'dinner', but only lunch & supper. Christmas & Thanksgiving were always 'dinner'.