IV is intra-veinous, meaning it is injected into the jugular vein of the horse.
IA are intra-articular and are injected directly into the joint. Legend, Pentosan and corticosteroids can all be injected IA.
Adequan, Pentosan and Legend each have specific functions within the joint, and some may be ineffective for certain OA (osteo-arthritis) while others are highly effective, it is worth it to do some research about their functions. There are many other injectables as well, like glucosamine, tildren, etc..
Talk to a lameness specialist vet. A comprehensive joint management program requires a lot more than an ineffective feed through supplement, and any vet that recommends one is not a lameness specialist, IMO. My vet has not once recommended a feed through supplement other than a high quality multivitamin and mineral supplement.
They say money doesn't buy happiness -- well happiness doesn't buy horses!