This will probably not disambiguate at all: http://www4.uwm.edu/FLL/linguistics/dialect/staticmaps/q_96.html

I remember thinking this was weird as a kid too. Some people around us (mostly mom's family, who moved to more rural IL from Germany) used "dinner" to mean a larger midday meal. Others didn't use "dinner" for that and would just say lunch regardless of size. I think my parents use dinner and supper interchangeably? I don't think I say "supper" at all?