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:
Κύριε Ἰησοῦ Χριστέ, ὁ Θεός μου, ἄνες, ἄφες, ἱλάσθητι καὶ συγχώρησὸν μοι, τῷ ἁμαρτωλῷ καὶ ἀχρείῳ καὶ ἀναξίῳ δούλῳ σου, τὰ πταίσματα καὶ πλημμελήματα καὶ παραπτώματά μου...
Maybe it is possible to set those greek words in order according to the gravity of a sin (mistake) they imply?