Fair is used in County which is a part of the State. I live in Kings County in California. Once a year, the farmers, teenagers have a FAIR .. where the animals are judged, food and home made things.
Exhibition is a show of new items to bring into the market. Like new smart phones.. new electric cars ..
TRADE show is like gun show where there are different ones who want to TRADE or Sale the items. Comic trade show ..
Does this help you?