The Greek word for sin is not the issue in 1 John 2:1 [1] and 1 John 3:4-8 [2]. The issue is the verb tenses.
In 1 John 3:4 [3] it reads: "Everyone who is practicing the sin, also is practicing the lawlessness." Notice in the literal translation, "practicing" is the translation of the present participle which denotes a lifestyle or continuous, ongoing condition. In the second clause, the present indicative verb is translated "is practicing" which also represents a present, ongoing condition. Both the word for sin and for lawlessness have the definite article "the" representing the principle of sin which happens to be explained in verse 1 John 3:8 [4] where it says, "The devil is sinning from the beginning." The devil is the sinner who energizes people to sin (See Ephesians 2:1-3 [5]).
In verse 1 John 3:6 [6] it reads, "Everyone abiding in Him is not sinning; everyone sinning has not seen Him, nor has known Him." Again the present participle is represented by the word "abiding" and expresses a present continual condition. This person is described as "not sinning" which again a present indicative verb expressing that the person who is dwelling in Christ does not habitually sin.
Then, in verse 1 John 3:8 [7] we have, "The one practicing the sin, is from out of the devil (as a source); because the devil is sinning from the beginning. For this purpose the Son of God was manifested, in order that He might loosen the works of the devil." Here, John states that the person who is in a continuous condition of practicing sin is spiritually functioning from out of the devil as a source, but the Son of Man came to loosen the works of the devil. When the Lord Jesus comes into a person's spirit, He literally loosens the power and influence that the devil has on a person and the devil is replaced by the Holy Spirit. Because the Holy Spirit resides inside of the believer, the believer cannot practice sin any longer because the spiritual force that forced the person to live a life of continuous sin has been removed and the Holy Spirit convicts the believer of sin.
Verse 1 John 3:9 [8] tells us, "Everyone who has been born from out of God (as a source), is not practicing sin, because His seed is abiding in him, and he is not able to sin, because he has been born from out of God." Verse 9 states, again, that a person born from out of God is not practicing sin, which is expressed by another present active verb denoting present continual practice. Then John states the reason he cannot practice sin is because God's Seed is in him. With God's Seed continually abiding in him, he does not have the ability to continually and habitually sin, "because he has been born from out of God."
In 1 John 2:1 [9] the literal translation reads: "My children, these things I write to you, in order that you should not sin; and if anyone should sin, we have an Advocate with the Father, Jesus Christ the righteous." John states that he is writing so that they "should not sin." The verb tense here is an aorist subjunctive. This means that John is referring to an act of sin, not a lifestyle of sin. Then he states, "If anyone should sin," again, using an aorist subjunctive expressing an act of sin. If anyone should commit an act of sin, we have an advocate (defense lawyer) in Jesus Christ who will intercede for us.
In summary, the person who does not know Christ habitually lives a life of sin because he is being energized by the spirit of the devil to fulfill the desires of the flesh and of the mind (again see Ephesians 2:1-2 [10]). When the Spirit of Christ comes into a person's spirit, the spirit of the devil can no longer cause that person to continuously sin against God. The Seed, or the Life, of God living inside of the believer prevents the believer from continually and habitually sinning against God.