It is actually quite simple.
Faith in Christ brings salvation - the outworking of salvation is good works.
Good works, holy deeds, righteous living are as a result of true salvation - do we always get it right no. Hence Paul's struggle with the flesh. We are not perfected the instant we are saved - we are changed slowly (sometimes fast) through the work of the Holy Spirit - called sanctification.
True Christians hate it when they sin, non Christians are oblivious to sin. What is the difference between non Christians and Chrisitans - both are sinner but one party is declared righteous through the sacrifice of Christ and is seen as sinless.
True Christians do works because they express mercy and justice in the image of Christ, they are not saved by works, that was accomplished the moment they put their faith in Jesus.
Very well said my friend!