I also work with horses. The product you are talking about, Adequan, is a poly-sulfated glycosaminoglycan (PS-GAG) which is related to a family of other GAGs. Hylaluronic Acid is a GAG. The veterinary equivalent is Legend, which is an IA(into the joint capsule) or IV, and Hylartin V, which is an IA. There are, of course, other "off-labels," but those are the only ones that are aproved by the FDA.
Anyway, the science with horses seems to be superior than humans when it comes to HA. First of all, the two injectables for humans (Synvisc and Hyalgan) are both IA only. Also, both are derived from roostercomb source, which leads to protein-contamination and the possiblity of allergic reactions. Legend for horses comes from a sterile bio-fermentation process.
Also for horses, oral HA is the new big thing that seems to be far more advantageous to injections. There is now oral HA supplements for people, but it hasn't caught on with MDs as it has with veterinarians. I actually have to go to my vet to get my joint supplement! I take one called Conquer III, which is made by the same company that developed the original oral HA for horses, Conquer.
Good luck in vet school!