Explain the difference between BY faith and THROUGH faith

Explain the difference between BY faith and THROUGH faith

Rom 3:30  Seeing it is one God, which shall justify the circumcision BY faith, and uncircumcision THROUGH faith. 

In the scripture above, Paul writes an interesting thing. He distinguishes between the circumcised and the uncircumcised by referring to their justification as by faith or through faith. So, what is the difference? Can this be explained and clarified? Many commentaries simply conclude that there is no difference between the two, but why then would Paul, through inspiration, write different words for each group. I do not agree with these commentaries as I believe that they are different, as much so as the doctrine between Israel and the Body of Christ are different. I am no formal scholar of doctrine and hermeneutics, so I do not claim absolute accuracy in my interpretation, but I have come to believe that Romans 4 has some insightful content to clarify this difference. 

Rom.4:11-17 And he [Abraham] received the sign of circumcision, a seal (Eph.1:13) of the righteousness of the faith which he had while still uncircumcised, that he might be the father of ALL those who believe, though they are uncircumcised [Gentiles], that righteousness might be imputed to them also [as the Body of Christ], 12 and the father of circumcision to those who not only are of the circumcision [Jews], but who also walk in the steps of the faith [Little Flock] which our father Abraham had while still uncircumcised.

The verses above connect Abraham to both the Jews and the Gentiles. The element of connection is faith which brings justification. Paul is saying that Abraham, who demonstrated this faith that led to righteousness (justification), is the example to both the Jews and the Gentiles. Regarding the Gentiles, since righteousness was given to Abraham BEFORE he was circumcised, the Gentiles can trust that by believing in Christ, they have the assurance of justification from God, like Abraham got. For the Jews, he is the example, not only because they are under the blessings of the covenant of circumcision, but they too can be saved by the same faith alone as Abraham demonstrated, without the need of the law, since Jesus had already died and risen and the new covenant was now in effect for the Israel of God, the little flock. [ie: the 'little flock' (Lk.12:32), those Jews who believe in the identity of Jesus (as their Messiah). Rom.2:25-29; Rom.9]  

13 For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith. (See Gal.3:6-9) …16 Therefore it is of faith that it might be according to grace, so that the promise might be sure to ALL the seed, not only to those who are of the law [Jews], but also to those who are of the faith of Abraham [Gentiles], who is the father of us ALL 17 (as it is written, "I have made you a father of many nations") in the presence of Him whom he believed—God, who gives life to the dead and calls those things which do not exist as though they did;

The above verses continue to confirm that justification by faith is available to both Jew and Gentile because of the cross of Christ. To the Jew by demonstration of THEIR OWN FAITH in their covenants, laws, and promises, and to the Gentile through having faith in what Christ has done for them, or in other words, NOT BY THEIR OWN FAITH but through the faith of another man, Christ.