So far I have given one sense in which Christ’s death is for the world. Here’s one more.
Christ’s death is applicable to all without exception. Let’s define applicable as it is used in this sentence. Here’s a pretty asinine illustration of what I mean:
I wear size 34 x 30 pants. I own several pairs of pants that are this size. There are other people in the world who would wear the same size pants as I do. My pants are applicable to them, but they are not for them.
So when I say that Christ’s death is applicable to all men, I say that it is sufficient for them and that it fits their situation, but yet it is not for all men. It is all that is needed for everyone’s salvation, but it’s being applicable does not imply it’s application. In other words, what Christ did on the cross was enough to save all men and is applicable to all men without exception, but it is not actually and really applied to all men without exception.
Here is where Arminian and Calvinist thought diverge. The Arminian will say that it is applicable to all, offered to all, and contingent upon any given person’s faith and repentance is applied to said person.
The Calvinist will agree with the Arminian but add that since Scripture teaches that only those who have been predestined to salvation will be regenerated and actually be able to believe and repent, that Christ’s death in a salvific sense is intended solely for them. When Christ died He had a specific group of people in mind, and in that group, specific individuals since a group does not exist apart from the individuals who make up that group.
This does not imply that the sufficiency of Christ’s death is diminished, but that the efficacy of Christ’s death is maintained. Christ did not entertain the possibility of failure on the cross. In fact, He only ever believed that He would be successful in His death. And at His death He gave a shout of victory. “It is finished! I have won!”
Christ has won. He did not negotiate a treaty. He won and did not give up any ground in what He intended to accomplish, which was the salvation of His people.
Soli Deo Gloria