It would be interesting to have some passages to compare from these authors that you speak about. I too would say, intuitively, that they can't mean exactly the same. So I put my head into some books (not really) to see what I can come up with. I do not find my finding interesting enough to earn a bounty, but nonetheless I prefer to share.
What I did find interesting was this distinction by Cicero from the Wiki on "duty":
Cicero, an early philosopher who discusses duty in his work “On Duty", suggests that duties can come from four different sources:
as result of being human
as a result of one's particular place in life (one's family, one's country, one's job)
as a result of one's character
as a result of one's own moral expectations for oneself
It also states:
Various derivative uses of the word have sprung from the root idea of obligation, a concept involved in the notion of duty; thus it is used in the services performed by a minister of a church, by a soldier, or by any employee or servant.
The concepts thus seem to be interwoven. The Wiktionary on obligation and duty provided me with information on the etymology of the words.
Obligation: From Latin obligatio, from obligatum (past participle of obligare), from ob- to + ligare to bind, from Proto-Indo-European *leig- (“to bind”).
Duty: From Middle English duete, from Old French deu (“due”), past participle of devoir (“to owe”), from Latin debere (“to owe”), from de (“from”) + habere (“to have”).
But what's really interesting is this Pdf on legal terminology I found. It states that even from a legal point of view, there is uncertainty about the use of these terms. I quote:
The terms ‘obligation’ and ‘duty’ are sometimes used as synonyms. They refer either to the
entire contractual relationship between the parties or, more narrowly, to what is due by the
obligor to the obligee.
Under American law and English law, as under French law, an informal consensus would
appear to have emerged, to the effect that the terms ‘duty’ and ‘obligation’ are synonymous.
For instance, the term ‘obligation’ in the singular or ‘obligations’ in the plural is univocal
when it refers to what one party has agreed to perform under the terms of an agreement. In this
sense, the positive counterpart of the obligation is the right (‘rights and obligations’), that is to
say what the creditor is entitled to receive from the debtor. This is a classical view of the term
‘obligation’ seen as ‘a tie which exists between at least two individual persons which enables
one person to request something from the other’1. The obligation should therefore be perceived
as including a legal tie, a legal tie between at least two persons and a coercitive power enabling
the enforcement of the obligation.
The area covered by duties is wider than that covered by obligations. A duty may be owed to a
person other than the other party to the contract. This distinction is in fact applied in English
law, in order to define the duty of confidentiality.
It would be useless to quote the whole paper, though I really think that it might answer your question. That leaves me to say that, though it might have seemed to you that they're not used synonymously, both the encyclopedia and the legal praxis claim they pretty much are. As you already figured out, your first thought, namely that "duty" might entail an action, is not right, because of the negative duties. Both concepts can refer to the human as human or to specific qualities. Both have, even etymologically, a reference to the object of the duty/obligation. No difference, even there. There might be a little legal difference, for it seems you can have duties that aren't part of the contract's obligations, but that should have no impact on philosophical jargon, I reckon.