The difference is that the twelve Apostles will be on twelve thrones judging the twelve tribes of Israel.
12 (and multiples of it) is an important number for Israel. It is a significant number throughout the Bible, and it always relates to Israel in some way.
Genesis 25:16 (KJV) These [are] the sons of Ishmael, and these [are] their names, by their towns, and by their castles;
twelve princes according to their nations.
What's being said is that the gospel of the kingdom for the nation of Israel is not the same as the gospel of grace for the whole world.
What is preached to the Jew (prior to Paul, mind you) is different than what is preached to the Gentile (after Paul's conversion).
But what was preached to the Jew after Paul’s conversion? Even Peter had to admit Paul had good things to say to the Jew.
2 Peter 3:15 (KJV)
And account [that] the longsuffering of our Lord [is] salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you;
Cornelius was saved AFTER Paul's conversion. That makes him saved via the gospel of Grace, and was preached Jesus Christ as Lord of all (Acts 10:36), and how He was raised on the third day (Acts 10:40), and that, through His name, whoever believes in Him will receive remission of sins (Acts 10:43).
Romans 10:9-13, or an early version of it, perhaps.
The point is that Peter was preaching the same gospel of grace to Cornelius that Paul was preaching to other Gentiles. Peter’s gospel was the same as Paul’s. I admit that Peter and the other apostles were not quick to switch to the grace gospel, or to leave behind what they were comfortable with, but they were doing it.
What we KNOW is that Paul, and Peter, James, and John, agreed to go to different groups:
But on the contrary, when they saw that the gospel for the uncircumcised had been committed to me, as the gospel for the circumcised was to Peter(for He who worked effectively in Peter for the apostleship to the circumcised also worked effectively in me toward the Gentiles),and when James, Cephas, and John, who seemed to be pillars, perceived the grace that had been given to me, they gave me and Barnabas the right hand of fellowship, that we should go to the Gentiles and they to the circumcised. - Galatians 2:7-9
Going to different groups is by no means the same as preaching a different gospel.
Rather, the reason for John not to go to the Gentiles is that his message wasn't FOR the Gentiles, but only for Israel. Remember, Christ said that He would return soon. Which meant that those who were saved under the gospel of the Kingdom needed to be ready for His return.
Paul thought Jesus would return soon as well. So those saved under Paul’s teaching ALSO had to be ready for His return, just as we do today.
No, they didn't. At least, not at first they didn't.
I appreciate the admission that they eventually, at least, preached the same gospel. I would suggest that the gospel Peter preached was always the same gospel, but there might well have been different messages for the Jews than for the gentiles—just not different gospels.
What difference in culture?
Paul was a Jew just as much as Peter was.
Unless you mean Jews vs Gentiles, in which case I would like to point out that the gospel that was revealed to Paul wasn't done all at once, and it would have taken even Paul some time to sort things out, especially because He was the first one to preach it.
Paul would have adjusted his message, and his behavior, if necessary, to fit his audience. 1 Corinthians 9:20 (KJV) And unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law;
though I caution you against appealing to tradition, which IS a logical fallacy.
You’ll have to throw out the whole canon of scripture, then, as we rely on tradition, primarily, for which ones are included.
We don’t throw out useful information just because it isn’t in scripture, though we treat it with proper skepticism.
And I didn’t appeal to tradition only, but compared it to scripture, I.e., the first 3 chapters of Revelation.