Ἁμαρτία is the most common greek word meaning “sin”, but in fact it has several synonyms. These are ἁμάρτημα, πταῖσμα, πλημέλλημα, παράπτωμα, σφάλμα. They all have “mistake” as a neutre meaning and “sin” as a religious one. I don’t think they all can mean absoltely the same because some of them can be met in a text together. As an example I would like to quote the beginning of a prayer:
I find using the big Liddell and Scott useful when parsing synonyms. Unfortunately, unless you have access to a library, buying one new is several hundred dollars. Fortunately, you can also use the Perseus Project search tools (http://www.perseus.tufts.edu/hopper/search).
Regarding your questions, the LSJ has the following definitions:
Ἁμαρτία = a mistake; in religion, a sin
ἁμάρτημα = a failure; a bodily defect; a sin
πταῖσμα = stumble, false step, mistake
πλημμέλημα = a fault, trespass
παράπτωμα = a false step, a defeat, a transgression
σφάλμα = a stumble or false step; also, a defeat or an error
As you suspected, they all have the basic idea of a “mistake” or a “sin,” but with different shades of meaning. παράπτωμα for instance also means “error in amount of payments,” perhaps suggesting some more venial mistake rather than a deadly one. Without researching the actual use of these terms in specific contexts, this is the best I can give you. Perhaps a priest could chime in?
In the slavonic translation of the prayer cited above it is a fall i. e. quite a serious sin as one can guess. Isn’t it a derivate from the verb πίπτω?
Paul (Rom 5:17) uses παράπτωμα to refer to the sin of Adam which brought death to the whole world. A more deadly sin was never committed before or since.
ἁμαρτία and ἁμάρτημα are used interchangeably in the NT. (Formally, of course, the former is the act of sinning itself while the later is the resulting sin that is produced from the act of sinning, but in the real world these distinctions often do not hold up.)
Have you thought of buying second-hand? More paper copies than ever come up for sale these days. I’ve seen several ninth editions go for under £50 on a certain online auction site this last year. What’s more the newer printings are generally of inferior quality to the older ones, so from the point of view of legibility you’d be better off with an older copy anyway.
re Victor’s comments on used unabridged Liddell and Scott, I just got one used from a dealer through Amazon. It was $120 US total for the two volumes. They’re old, but still in great shape, and there seems to be quite a few out there for purchase. Can’t beat the unabridged if one wants to make the deep plunge!
Less point in buying LSJ now that it’s online for free (see mstrebe’s post) unless you want to make annotations in it.
To figure out the differences in underlying meaning it’s always useful to look at the corresponding verbs (paraptwma < parapiptw, yes). But of course word meanings are not entirely stable.
I reckon it would be a mistake (if not a sin) to make any sharp differentiation between them in a context like this. Just as you have a trio of alliterative epithets for doulw, so you have second alliterative trio here. The verbs themselves constitute a trio too, the anes & afes pair followed by a magnified third member (sugxwhrson). It’s all just a padded-out version of “Forgive me my sins” (cf. Lord’s Prayer). There are very similar things in prayers/curses in magic. Prayers like to cover all the bases, and it sounds good. Stylistics trumps semantics.
Interesting, this certainly shows the limited utility of relying solely on the dictionary.
Re Victor and ailuros, the only used copy I have found in the last year was $50 and it was falling apart. Luckily, for those interested, another forum member discovered Oxford is selling the LSJ new for $65, which comes out to $75 with shipping and tax. http://discourse.textkit.com/t/lsj-on-sale-in-us-for-65-brand-new-from-oup/12236/1
One of the advantages of the paper version over the digital (it’s a small one, I admit) is that you can see the whole spread of entries on the double-page you happen to be open at to view the entry you’ve searched for. This can sometimes be vitally instructive in a way that seeing an entry in isolation is not. Of course there may be a way of simultaneously viewing a whole double-page spread of entries on Perseus, but if there is I haven’t figured out how to do it yet. The same applies to Smyth’s Greek Grammar and various other books I regularly consult on Perseus.