No, I was not being glib. The Roman doctrine of original sin comes from St Augustine. He said it was hereditary and theorized it passed through the man's seed. There is no matching idea in the East.
You have to understand the context in which the notion really became fleshed out. St Augustine was correcting Pelagius' wrong teaching that each man was born into innocence (like Adam) and was capable of achieving salvation on his own - through the Law, potentially. Part of this was, I believe, Pelagius' own desire to show just how terrible humanity really is: after all, if you can be good but aren't, isn't that worse than if you can't?
St Augustine disagreed -- with good reason. While he complimented Pelagius' austere way of life and serious monasticism and no doubt agreed that there was a need for continued moral growth in the faithful, he saw that there was a spiritual danger in the teaching. Namely, that Christianity was not merely a system of moral living that led to salvation. He wrote to guard the faithful against these errors. St Augustine was enlightened, and was not writing based on pure logic or philosophy but out of his own experience with God -- because he knew that the Pelagians were not writing from the same experience. However, at the end of the day St Augustine was separated from the theological inheritance of the Fathers by geography and language, and some of the ways he expressed these truths were not in line with patristic tradition in the East.
This is why St Photius calls him blessed and says subsequent people in the West overstate and misuse his writings. St. Gregory of Nyssa says that we should not "insert our errors of speech" into "theological doctrine." In other words, he was aware that there exists the danger of expressing something wrongly and its being taken as doctrine. We should be careful with confusing St. Augustine's "errors in speech" with "errors in doctrine" or an absence of pious and enlightening experience of the Mysteries of God.
Anyway, the how of St Augustine's correction were basically that there are two aspects: vitium and reatus. Vitium is the inherited moral deficiency, the corrupted will by which post-lapsarian man can choose only sin, and can choose no good. Reatus is the inherited legal liability, that Adam condemned mankind along with himself.
The big discussion, then, is really about two things: do we have a truly free will? Can we choose good? And, second, are we heirs to Adam's guilt along with the consequences of it (death, fallen world, so on)?
The East doesn't really agree with either aspect of St Augustine's teaching, and certainly rejects the centuries of building on these ideas that subsequent Western theologians did.