In theory, different words are meant to describe different types of events.
Virtual Trade Show, as name implies, is an event where companies in a specific industry gather to showcase and demonstrate their new products and services. In general Virtual Trade Shows are business-to-business (B2B) type of events; they are not open to the public and are meant to be attended by company representatives, industry officials and (of course!) press. Usually Virtual Trade Shows are organized and sponsored by trade associations for specific industries, so they are perfect networking platforms for industry professionals.
Virtual Trade Fair, on the other hand, is more business-to-client or customer (not only consumer!) type of event. Companies gather not only to showcase their products and services, but also to sell and market them. Virtual Trade fairs (or simply Fairs) are open to anyone interested and can cover a few industries at the same time. They tend to take place over 3-5 days, sometimes even longer.
Virtual Exhibition has the least of sales element in it; the primary objective is to showcase products and services. Usually Virtual exhibitions cover one industry at a time and are geared towards building general image of a company/brand.