For humans: I have a ruptured disc in my back, I asked the Consultant what the difference was between a physio and osteopath/chiropractor. He said in the old days the physio gave you exercises to help get over an injury and the osteopath/chiro manipulated you. He said that now, there is a lot of overlap in the professions as Physios will do some manipulation and osteo/chiro also give you exercises to do. My physio says that the professional chiro and osteo bodies are amalgamating, so they will soon become one professional body.
Physios are more movement and manipulation and muscles, usually for rehabilitation and care - you can do physiotherapy exercises on your own, as suggested by your physio. Osteo and chiro is skeletal (chiros are more to do with backs and spinal stuff). My current osteopath likes to twist and snap things straight and then do some deep muscle massage to get everything to relax and stay the way it should. The physio hurt more than the re-aligning last time!
My physio also does 'back cracking' (sorry, manipulation) and accupuncture as well as more traditional physio. I think there is a lot of cross over and cross training, you just have to find what methods work best for you.