subrogation : step in another's shoe. Your auto insurance company would sue the other party by "step in your shoe", whatever they got from the other driver they pass it onto you. That's a subrogated claim. (I understand this is not how you get paid, you went through the other insurance comopany).
Your disability insurnace didn't sue anybody, therefore disability payment is not from a subrogated claim.
third party claim: A pays you for pain and suffering, medical cost and loss of wage. Disability company pays your loss of wage as well. Therefore you are double paid on the issue of "loss of wage". Disability company want part of their payment back because a third party is paying your loss of wage. The third party claim is from the disability company to the other driver.
Compare your case with another worker who got cancer and had to claim disability, there is no third party (like another drive) to be responsible for the disability therefore it was not a third party claim.
