The dispensationalists I know hold roughly the following: After the resurrection, God expected Israel to convert through the teaching of the Apostles, whereupon Jesus would return and inaugurate an earthly kingdom in Jerusalem, under which obedience to the law would still be a requirement for salvation. This plan A didn’t work out, and after the stoning of Stephen God gave up (or at least postponed) plan A and implemented plan B, by converting Paul and giving him a different gospel to preach, the gospel to the Gentiles. The “plan A” gospel can be found in the preaching of Jesus and the letter of James and other places in the New Testament - pretty much anywhere you see the bible teaching good works play a role in our salvation. The “plan B” gospel, the “gospel of grace” is found in Paul’s writings, teaching that we are saved by grace apart from works.
The whole thing is an interesting variant on the standard Protestant theology, in that it gives it’s adherents the ability to come to grips with the clear teaching of Jesus, James, etc., on the necessity of good works (instead of trying to twist these to mean something else, as standard Protestantism does), but still say those teachings don’t apply to them, because they’re under the “dispensation of grace”. Unfortunately, the whole “2 gospels” theory is utterly unbiblical and totally without support in the early fathers.
“1 Now I make known to you, brethren, the gospel which I preached to you, which also you received, in which also you stand, 2 by which also you are saved if you hold fast the word which I preached to you, unless you believed in vain. 3 For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, 4 and that He was buried, and that He was raised on the third day according to the Scriptures, 5 and that He appeared to Cephas, then to the twelve. 6 After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; 7 then He appeared to James, then to all the apostles; 8 and last of all, as to one untimely born, He appeared to me also… 11 Whether then it was I or they, so we preach and so you believed.” 1 Cor 15
THE (singular) gospel, the one by which you are saved, is preached by “I or they”, that is , Paul, Cephas, James, the 12, and the 500.
“6 I am amazed that you are so quickly deserting Him who called you by the grace of Christ, for a different gospel; 7 which is really not another; only there are some who are disturbing you and want to distort the gospel of Christ. 8 But even if we, or an angel from heaven, should preach to you a gospel contrary to what we have preached to you, he is to be accursed! 9 As we have said before, so I say again now, if any man is preaching to you a gospel contrary to what you received, he is to be accursed!” Gal 1