If you get knocked off something, than means you were previously on the thing that you got knocked off.
I was sitting on a horse. I got knocked off the horse.
When you are knocked down, you fall to the ground. Sometimes, you can be knocked down at the same time you are knocked off something (e.g. a horse), but one does not automatically mean the other.
Maybe a different example to clarify:
Thomas was standing on the train. A heavy gentleman bumped into him. Thomas fell to the train's floor.
Thomas was knocked down (because he fell to the floor).
Thomas was standing on the train. A heavy gentleman bumped into him and pushed him off the train.
Thomas was knocked off the train.
Thomas was standing on the train. A heavy gentleman bumped into him. Thomas lost his balance and fell onto the train platform (= he fell out of the train). The train left before Thomas could get back on it.
Both are true. Thomas was knocked down (because he fell onto the ground of the train platform), but he was also knocked off (because he was previously on the train, but not anymore).