Not all without exception but all without disctinction

The idea is that Christ death was a death that went out towards different kinds of people not just towards certain kinds. As was the case for the old dispensation where God chose a people for Himself to further out His redemptive purposes. Jesus was born of the Jewish religion not of the Greek system where the belief was pagan. Jesus was a Jew. Salvation was from the jews scripture says. To the Jew first then to the Greek. The Jews were God's chosen people in that the Messiah came from them (Romans 9:1-5). Of course this does not mean that under the old testament dispensation that there were no pagans who were brought from Darkness to Light. However, they had to become Jewish. An offshoot of this is that the Christians in Acts were wondering whether to make Gentile Christians to first become Jews so that they could become Christians. But the conclusion made was no for salvation is by Grace Alone which is the point of the letter to the Galatians.
Of course the wall of seclusion was not knocked down until after Jesus accomplished his mission. The seclusion was that only the Jews were God's people and anyone outside of Jewish community were considered filthy.
The statement made in John 3:16 was astounding for the purpose - John writes was to show that God qualitative love was not just toward the Jewish audience but extended out toward the rest of the world of the gentile. So when scripture makes reference that Christ died for all people it should really be read as all kinds of people. The atonement was in fact particular in intent in that God purposed that Christ should die for the salvation of His elect those whom He had Chose since before the foundation of the world who were spread abroad throughout the world.
The good news is that now the gospel is for all kinds of people. it is not just for the wealthy or the poor people but all people are to repent of sin and trust in Christ for righteousness sake. 1 Timothy 2 speaks of this truth. So today where one might be born in a Christian home the temptation might be that because He is of the Christian family he is saved. This is not true at all. Scripture says for all have sin and fall short of the glory of God. Therefore all must find there refuge in Adam number two. The idea is that as we preach the gospel to all people only those whom the Father has chosen to come to faith in His Son Jesus Christ will come by the regenerating work of the Holy Spirit who works so graciously and free (Ephesian 3:14-19).
Now this by no means says that Christ died for all men without exception that all men everywhere universally have been bought with a price by the blood of Christ for certianly He died for only His elect people whom God chose most freely in eternity past. Only God's elect will come to faith at the hearing of the gospel at the particular point that God decreed. The reprobate will be hardened by God's good providence.

A good book to read on this subject is Abraham Kuyper's Particular Grace

Logical Order of Decrees

In the Supralapsarian camp God determines to save some (The elect unto salvation) and others not to be saved (The reprobate unto condemnation). According to the Supralapsarian position, "God, even in the decree to create and permit the fall, had his eye fixed on His elect individually, so that there was not a single moment in the divine decree, when they did not stand in a special relation to God as His beloved ones." Louis Berkhof. Thus although the divine decrees are different and distinct nothing frusterates His plan in accordance to the Supra position for God's plan to magnify his glory by the salvation of some and pertition of others will be played out. Where as in the infralapsarian position the decree are distinct and seperate. "Infralapsarians, on the other hand, hold that this personal element did not appear in the decree till after the decree to create and to permit the fall. In these decrees themselves the elect are simply included in the whole mass, and do not appear as the special objects of God's love. In other words all of humanity were sinners and so from the mass of fallen (sinful) man God's elect were chosen. This is ultimately the question which comes out of this - was "the fall in reality a frustration of his plan?" because in the scheme of things God first "decrees to create the world for the glory of His name, which means among other things also that He determined that His rational creatures should live according to the divine law implanted in their hearts and should praise their maker. Then He decrees to permit the fall, whereby sin enters the world. This seems to be a frusteration of the original plan, or at least an important modification of it, since God no more decrees to glorify, Himself by the voluntary obedience of all His rational Creatures." So that in the Infralapsarian position God is changing what He wills.

The Supralapsarian "Will speak of predestination unto the grace of God in Jesus Christ, but not of a predestination unto sin." - Louis Berkhof

This means that the reprobate fell by their own will. That Sin was the work of Man and not of God, but God ordained that Man would fall.

On the false notion of Becoming an Elect child of God.

My professor once said that when he comes to faith in Christ that it is at that moment in time that he has become God's elect. Partly after hearing my professor and reading this excerpt from Louis Berkhof from what it sounds like the view is saying is: That God has elected the Church for salvation and anyone who does not fall into the salvivic camp in the Church by faith in Christ is a reprobate and anyone who does so is an elect. Now I think the problem here if this is actually what the view is saying is that it is misusing the terms: Election and Reprobation for the Church and the Lost.

"Camfield therefore says in his Essay in Barthian Theology, entitled Revelation and the Holy Spirit: 'It needs to be emphasized that predestination does not mean the selection of a number of people for salvation and the rest for damnation according to the determination of an unknown and unknowable will. That idea does not belong to predestination proper.' Predestination brings man into crisis in the moment of revelation and decision. It condemns him in the relation in which he stands to God by nature, as sinner, and in that relation rejects him, but it chooses him in the relation to which he is called in Christ, and for which he was destined in creation. If man responds to God's revelation by faith, he is what God intended him to be, an elect; but if he does not respond, he remains a reprobate. But since man is always in crisis, unconditional pardon and complete rejection continue to apply to every one simultaneously. Esau may become Jacob, but Jacob may also become once more Esau. Says McConnachie: 'For Barth, and as he believes, for St. Paul, the individual is not the object of election or reprobation, but rather the arena of election or reprobation. The two decisions meet within the same individual, but in such a way that, seen from the human side, man is always reprobate, but seen from the divine side, he is always elect....The ground of election is faith. The ground of reprobation is want of faith. But who is he who believes? And who is he who disbelieves? Faitand unbelief are grounded in God. We stand at the gates of mystery.'"

Pg. 111