Many philosophers have sought to distinguish moral obligation from moral responsibility. In this book, author Ishtiyaque Haji argues that these concepts, though still distinct, are more similar than many think.
First, conceptual ties between obligation and responsibility speak largely in favor of responsibility's requiring alternatives, challenging the view that responsibility does not require freedom to do otherwise. Second, many philosophers champion responsibility semicompatibilism, which mean that even if determinism is incompatible with the freedom to do otherwise, it is compatible with responsibility. Essential relations between obligation and responsibility are deployed against this thesis, and the parallel thesis of obligation semicompatibilism is also rejected. An upshot of forsaking these two species of semicompatibilism is that determinism threatens both obligation and responsibility by eliminating alternate possibilities. Third, many concur that whereas you may now no longer have an obligation that you previously had, you cannot now fail to be blameworthy for something for which you were formerly to blame. Haji rejects this immutability thesis about blameworthiness.
Haji does find one legitimate difference between obligation and responsibility: while how one acquires one's values may significantly influence whether one is responsible for much of their conduct, obligation is not "historical" in this way.