Whats the difference ?

Whats the difference between the Righteousness of the Law or Works as Per Rom 9:31

But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.

Rom 10:5

For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them.

Phil 3:9
And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:

Or The Righteousness of Faith as Per Rom 4:11,13


And he received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also:

For the promise, that he should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith.

Rom 9:30

What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.

Rom 10:6

But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down from above )

Here is the difference in the Two, Righteousness of the Law or works is when we consider that God makes us Righteous based upon something we do, any act of ours qualifies, such as believing, repenting, accepting something, when thats the case its our own Righteousness we Trust in as Per Phil 3:9

And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:

Even if we claim Faith as our own Righteousness to be the cause as some pervert the understanding of this scripture Rom 4:5

But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for

If one by this verse teaches that his faith , his own faith is what caused him to be righteous,then they fall right into the saying of Paul in Phil 3:9 as having their own Righteousness Faith !

Now the Righteousness of Faith is when one has a Righteousness not of themselves revealed or made known to them, and that it is theirs by Free Gift Rom 5:17

For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.)

The Gospel reveals it to Faith Rom 1:16-17

16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.

17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.

The Righteousness that is revealed, is revealed to Faith,so how could it be their Faith ?

As a Result of this revelation to Faith we are persuaded to believe it by Faith. The word Faith is the greek word pistis and means:

conviction of the truth of anything, belief; in the NT of a conviction or belief respecting man's relationship to God and divine things, generally with the included idea of trust and holy fervour born of faith and joined with it

a) relating to God

Its from the word peithō:


persuade

a) to persuade, i.e. to induce one by words to believe

So the Righteousness of Faith is when one has an Gift of Righteousness revealed to them by God in the Gospel and this revealing persuades us to believe what is Revealed, the imputation of Christ's Righteousness made Ours as a free Gift.

And remember, Righteousness of the Law or Works is whenever we believe we are made Righteous by anything we do !