I must admit that I am confused with these two words. For so long a time, I have been using them interchangeably. I have consulted the dictionary (of course) but I can't seem to pinpoint the glaring difference between the two (if there is any). This may be similar to this question.
In many ways they are the same thing, but the "angle" is slightly different. Responsibilities are more intrinsic, as opposed to obligations. The latter, I think, is more something you have towards your environment, society,... surrondings basically. Allow me to explain why I see it like this:
If you have children, you are responsible for them, and therefore, you have the moral obligation to take care of them to the best of your abilities.
Note that you are responsible and this results in an obligation (in this case, a moral one).
Equally so, taking good care of your kids means good education, which in turn results in your being obligated to get them ready for school, help them if they need help, and, of course, pay for the tools the need (books, bills and the like)
In that respect, responsibilities are somewhat intrinsic to life: you are responsible for your own health and well being (eg: smoking is being somewhat irresponsible/reckless towards your own health).
If you, like me, are a smoker and have kids, I'd say you are obligated to smoke outside of the house, in order not to damage their health.
Your responsibilities are yours, but they result in obligations towards both yourself and your environment, or even society.
Sure, you might be given responsibilities. At work, or by people you care about, but these situations suppose a contract of sorts: a social or legally binding contract, which implies, in turn obligations. Basically: Responsibility and Obligation "go together like Horse and carriage, love and marriage": you can't have one without the other.
The inverse applies here, too: you are obliged to obey the law, if you don't, that causes harm to the society. If you get caught, and appear in front of a judge, you'll be held accountable for your actions (you are responsible for your actions, if you're a sane person).
So, a responsibility is something you can be held accountable for. How much you actually take responsibility for thinks, is evident from how you deal with your resulting obligations.
AHD includes these senses for 'obligation':
- a. A social, legal, or moral requirement, such as a duty, contract, or promise that compels one to follow or avoid a particular course of action. b. A course of action imposed by society, law, or conscience by which one is bound or restricted.
Thus in some cases, because one has a social or moral requirement but not a legal one say to perform some service, it could be argued that the person has and has not got an obligation to do it. The confusion of 'polysemy + hypernymy'. Sometimes, the compounds / collocations 'moral obligation', 'legal obligation' and 'social obligation' are used to specify the sense intended.
The senses of 'responsibility', as you infer, overlap to a large degree with those of 'obligation', but carry a little less of a legal flavour. Though if a contract you've signed says 'It is the client's responsibility to . . .', certainly don't assume that's not a legal requirement / obligation.