A retriever field trial is a competetive event with places awarded. They began around the 1930's (?) under the premise of "my dog is better than your dog". The rich and famous got involved, thereby bringing in pro trainers. Field trials have gotten more and more difficult over the years (necessary for determining which dog is the best, because trainers and dogs have improved over the years), and distances for marks and blinds are now in the 300+ yard range (last I heard). Because of the tremendous distances, handlers must wear white coats so their dogs can see them.
Hunt tests came along about 1984. A retriever hunt test (there are 3 organizations/flavors; AKC, HRC, and NAHRA) is designed more for the hunter and his dog, although pros are involved in these as well. The most important thing is that dogs do not compete against each other. They are evaluated against a standard. Either they pass or fail. Distances for marks are anywhere from "in yo' face" to about 125 yards. Blind distances are in the 40-100+ yard range. At HRC hunt tests, camouflage clothing is standard and white clothing is banned. HRC tests attempt to simulate realistic hunting situations. You handle a real shotgun (loaded with blanks) and "shoot" the birds (usually mallards) for your dog. You might be wearing hip waders and standing in thigh-deep water with your dog on a platform. Any waterfowl hunter with a good, steady, experienced meat dog, and a familiarity with the rules should be able to pass at least a "Seasoned" (mid level) level HRC hunt test.
That about sums it up. Would be happy to discuss details regarding HRC tests, since that is what I have the most experience with. I have run a few AKC Senior and Master tests, but I have never run a NAHRA test.
The non-breed specific retriever clubs that I know of in Ohio are:
Lake Erie HRC (north central)
Sandusky Bay HRC (north central)
North East Ohio HRC (northeast)
West Central Ohio HRC (west)
Ohio River HRC (southwest)
Ohio HRC (northwest)
Buckeye Retriever Club
? (there used to be one, but I believe it has gone under)
As you can see, you will have the greatest opportunities if you go with the HRC flavor in Ohio.