In Obligation and Duty – Two Things or One?, Lionel Smith examines whether obligations and duties are fully synonymous under Quebec civil law. He argues that they are not, saying that obligations are a subset of duties: every obligation is a duty, but not every duty is an obligation. He suggests this distinction is also present in English common law.
I remain skeptical of the extension to English common law. While lawyers routinely speak in terms of duties rather than obligations, it is not clear that this reflects a conceptual distinction rather than habit.