I'll give the basics on trials and hunt tests. The NAVDA guys and retriever guys will have to fill in what I can't.
Field trials: Dogs are judge for their performance. They are competing against the other dogs in the trial. There's only one winner. And there's second place and third place. All kinds of organizations run trials. AKC, NSTRA, Breed clubs.
Hunt test: Dogs are judge for their performance. The judges score them and they are competing to achieve high scores. Any and all dogs can achieve a qualifying score (but usually just some). Hunt tests are run by multiple retriever groups and the AKC.
NAVHDA: They use the hunt test scoring model.
Those are the basics. Hopefully people can fill you in on more.