Is there a difference between being righteous (before God) and living righteously?
Even though God, in and through Christ, grants us righteousness (perfect standing) before Him legally, he still desires our life to be ²lived righteously. It is only through ²righteous living we are in tune in our daily lives with who God is and most aligned with putting Him on display i.e. honoring and glorifying Him.
He created us to be aligned with his will (design) in our conduct, so we might experience more of Him and best put Him on display (honor or glorify Him) before others. This is the desired outcome of the good standing God has fully secured for us in Christ.
In fact, the whole intent of making us right with Him is so we will live righteously for His honor.
The idea of being made right in order to live right is expressed in several places but most often and clearly in Paul's letter to the Romans.
Romans 6:4 ESV
We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.
Romans 7:4 ESV
Likewise, my brothers, you also have died to the law through the body of Christ, so that you may belong to another, to him who has been raised from the dead, in order that we may bear fruit for God.
"There is therefore now no condemnation for those who are in Christ Jesus (i.e. we are perfectly right with God in Christ). For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death. For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us..." - Rom 8:1-5
Each of the above 3 passages shows the desired outcome of God making us right with him is that we will live righteously.
In fact, in several of Paul's letters (Ephesians, Colossians, ³Hebrews and Romans) the first part of the letter lays out what God has done for us, and the remaining part deals with how we are to conduct ourselves in light of this.
This is clearest in the book of Romans, where the first 11 chapters elaborate on our alienation from God and what He has done for us in Christ, then from chapter 12 on it shifts to how we conduct ourselves in light of this.
I appeal to you therefore (in light of what I have said up to this point regarding what God has done for us), brothers,[a] by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship.
This isn't a coincidence, it is because righteous living must always flow out of a righteous standing with God. This is clearly implied and stated explicitly in several passages.
For a further discussion on being right vs living right click here
What is the good news? click here
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Footnotes:
²What exactly is righteous living or living righteously? When our conduct is perfectly aligned with God's design and will. And what is God's design and will for us and all creation? That in everything we do and say we honor and glorify him. In doing so, we also experience our own significance - glory.
We will not value or love God above all others until we experience his value or love for us.
Which comes first our valuing and loving Him or Him valuing and loving us?
³There is good reason to believe Paul dictated the book of Hebrews to Luke, who wrote it. The way the letter flows and unfolds and the thorough knowledge of the OT is characteristics of other letters by Paul. But the style and elegance of the Greek used in the book is indicative of Luke.
There are several other reasons some believe Paul dictated it. Primarily because, as far as we know, all but one of Paul's letters (including Hebrews) was dictated. Also Luke was a highly educated Greek national and medical doctor, fluent in proper Greek. Hebrews was written with grammatical precision, using several words unique to the book of Hebrews. This was uncharacteristic of Paul's other letters but similar to the style used in the gospel of Luke. For these reasons, many think Paul didn't write it.
It is also believed that Paul deliberately did not identify as the author since he was considered the apostle to the Gentiles and not looked upon favorably by the Judizers within Jewish circles. Some suggest he left his name off to avoid any resistance to the letters' reception and circulation.