It actually depends on which vaccine you are talking about. If you are talking about the Rabies vaccine, then there is absolutely no difference. It is the same vaccine, just the length of time that the state, city, or vet says it is good for. (i.e., Some cities will require the Rabies yearly and others do not, the pet must have already had a rabies vaccine the previous year for the next one to be good for 3 years, etc.)
If you are talking about the DAP (parvo/distemper) vaccine then there is a little difference. Many vets will use a 1 year vaccine and say that it is good for 3 years. There is only one manufacturer of an approved 3 year DAP vaccine (so if you want a vaccine that's good/approved for 3 years then I would make sure which vaccine your vet is using). Intervet came out with the only USDA approved 3 year distemper vaccine (it is called the Continuum DAP). The main difference is that it has actually gone through the testing to become USDA approved. (One thing that I have noticed about this vaccine is that when it first came out, occasionally some of the smaller dogs seem to be more prone to reactions to it, but I believe at one time they had too much protein in their diluent and fixed the problem. Since then, the incidence of reactions has seemed to subside.) I personally like the 3 year DAP because I don't have to vaccinate as often. Both of my girls have had it and have had no problems. Hope this helps.