Answer
The important difference between Romans 2:12 and 3:9 with regard to sin is that the former talks about the “action” on our part and the latter talks about the “result” of such actions.
Explanation
Action:-
In spite of all the popular human-made definitions of sin, God Himself defines sin as the transgression of God’s Law:
“Whoever sins is guilty of breaking God's law, because sin is a
breaking of the law” (1 John 3:4).
This is the action mentioned in Romans 2:12.
Result:-
There are different levels of the result.
- First of all, they become under sin which is the immediate and direct result of the action of sinning:
“For we have charged both Jews and Greeks before, all with being
under sin” (Rom 3:9).
- To a person who is under sin, the sin “lords it over” him if he is not under grace:
“For your sin shall ………. lord it over you”, if you are not “under
grace” (Rom 6:14). (I have removed “not” without changing the
meaning)
- But if you are under sin, that is, when sin lords it over you, you are under Law:
“For your sin shall ……… lord it over you, for you are ……..
under Law” (Rom 6:14). (I have removed both “not”s without changing the meaning)
- When you are under sin, you are under Law and that means you are under the “custody” of Law:
“But before the coming of faith, we were guarded under Law, having
been locked up to the faith being about to be revealed” (Gal 3:23).
So, under sin means under Law. Under Law means under the custody of Law. The Law claims our life as a penalty. We have no right to live. It is this penalty of the entire humanity that Jesus Christ paid in full on the cross.
[Under Law does not mean under the “obligation” of keeping Law. Under Law means under the penalty of Law. This is a great misunderstanding on the part of antinomians]
- The Law claims our life as long as we live. But once we die, we are freed from the custody of Law:
“Or are you ignorant, brothers, (for I speak to those knowing Law),
that the Law lords it over the man for as long a time as he
lives?” (Rom 7:1)
- In Baptism we die together with Christ who died on our behalf as a penalty for our sins:
“Or are you ignorant that all who were baptized into Christ Jesus were
baptized into His death? Therefore, we were buried with Him through
baptism into death, that as Christ was raised up from the dead by
the glory of the Father, so also we should walk in newness of
life” (Rom 6:3-4).
In baptism, we receive the Holy Spirit as a free gift (Acts 2:38) and thus we receive a new life freed from the custody of law because:
“It is the Spirit that gives life” (John 6:63).
- Thus we come under grace of God freely because Jesus paid the penalty on our behalf. Now we live not a fleshly life but a spiritual life walking closely with God.
We are no longer under Law because by our death with Christ in baptism we are freed from the clutches of the Law. We are spiritual and are able to abide by the spiritual Law:
“But if you are led by the Spirit, you are not under Law” (Gal 5:18).
The people who are led by the Spirit are able to follow the "spiritual" Law.
Conclusion
So Romans 2:12 talks about the action on our part and Romans 3:9 talks about the result which then takes a series of steps until we become a new spiritual person through Christ.