Too often we think too narrowly on the subject of sin.
Transgression
H6588
פּשׁע
pesha‛
peh'-shah
From H6586; a revolt (national, moral or religious): - rebellion, sin, transgression, trespass
A transgression is a willful act of rebellion against an establish law. David’s transgression was adultery. He knew the law, and he crossed the line anyways. When the nation was following false gods, it was committing a transgression.
Is a transgression always a wrong? No. A transgression can be crossing the line concerning moral, physical, or national laws. If I am speeding I am transgressing the law of the land. What if I am a cop and I am speeding to catch a murderer, or a thief, or to get to the scene of an accident quickly? In these cases I am transgressing, but I am not committing a wrong.
For our purposes we need to focus on the wrongs. It is willfully ignoring the Word of God resulting in choosing to rebel against His Law and His authority. This impacts our relationship with Him, and as we see in Psalm 51 we need to rely on God to cleanse us from our transgressions.
Iniquity
H5771
עוון עון
‛âvôn ‛âvôn
aw-vone', aw-vone'
From H5753; perversity, that is, (moral) evil: - fault, iniquity, mischief, punishment (of iniquity), sin.
We do not know what David did to justify his actions, but he admits to iniquity being a problem that he needed God to handle in Psalm 51. What we do know for sure is that David twisted the Word in order to justify His actions. We twist the Word to justify our own iniquity. How often is gossip disguised as a prayer request or false concern for someone else? Some people pervert the Word to support racism or tax evasion. How about when we hammer on someone for taking a stand that differs from ours on a biblical issue, but we label it as contending for the faith? I am sure we can all see how iniquity is a “wrong” and it has a negative impact on our relationship with God. This perversion or twisting, of the Word, has a lasting impact on our character as this leads to established habits and sinful lifestyles. These impact future generations, for example we see racism being passed on to kids. Another would be the increased likelihood of kids being abusive or addicted to drugs and alcohol if those are issues for their parents.
I found the word “iniquity” in 2 places in the NASB. The first was in Peter’s rebuke of Simon the sorcerer in Acts 8. The second was as a description of the tongue in James 3. (OUCH! I see some good sermon material there, but for another day.)
Sin
H2403
חטּאת חטּאה
chaṭṭâ'âh chaṭṭâ'th
khat-taw-aw', khat-tawth'
From H2398; an offence (sometimes habitual sinfulness), and its penalty, occasion, sacrifice, or expiation; also (concretely) an offender: - punishment (of sin), purifying (-fication for sin), sin (-ner, offering).
The OT has few different words (8) for sin and they are built on
H2398
חטא
chata (306c); a prim. root; to miss, go wrong, sin: - bear the blame (2), bewildered (1), bore the loss (1), bring sin (1), cleanse (5), cleansed (1), cleansing (1), commit (2), commits sin (1), committed (21), done wrong (1), errs (1), fault (1), fear...loss (1), forfeits (1), indicted (1), miss (1), offended (1), offered it for sin (1), offers it for sin (1), purged (1), purified (2), purified themselves from sin (1), purify (6), purify him from uncleanness (1), purify himself from uncleanness (2), reach (1), sin (55), sin have I committed (1), sinful (1), sinned (87), sinner (7), sinning (4), sins (23).
The root of all the Hebrew words is chata, and means to miss or go wrong.
G264
ἁμαρτάνω
hamartanō
ham-ar-tan'-o
Perhaps from G1 (as a negative particle) and the base of G3313; properly to miss the mark (and so not share in the prize), that is, (figuratively) to err, especially (morally) to sin: - for your faults, offend, sin, trespass.
To sin is to miss the mark. Like an archer who launches an arrow at a target but it falls short. I intend to hit the bull’s-eye, I intend to love my neighbor, but I fail sometimes. This is sin. It is not rebellion. It is not intentional. It is not twisting the Word to justify myself and my actions.
Again, like the word “sin” in the OT we also find numerous words in the NT that build off of this key word.