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.
Based on the base word definitions:
as·sume
əˈso͞om
verb
suppose to be the case, without proof.
"you're afraid of what people are going to assume about me"
synonyms: presume, suppose, take it (as given), take for granted, take
as read, conjecture, surmise, conclude, deduce, infer, reckon, reason,
think, fancy, believe, understand, gather, figure
Versus:
pre·sume
priˈzo͞om
verb
suppose that something is the case on the basis of probability.
"I presumed that the man had been escorted from the building"
synonyms: assume, suppose, dare say, imagine, take it, expect,
believe, think, surmise, guess, judge, conjecture, speculate,
postulate, presuppose
So an assumption does not have any proof, whereas a presumption has some backing of proof in the form of probability or a "hunch".
More details can be found in this article.
Best Answer
Both are found, but there is no obvious difference in meaning. Similarity to is the preferred construction in both American and British English. The Corpus of Contemporary American English has 332 records for similarity to and 52 for similarity with. The figures for the British National Corpus show a less pronounced preference, but, with corresponding figures of 105 and 34, it is still significant.
The Oxford English Dictionary supports this finding with 103 citations for similarity to and only 14 for similarity with.