Jesus is the Savior of the world according to John 4:42 and 1 John 4:14.  

According to Calvinists, the word kosmos in those verses refers to the world of the elect. In other words, He is the Savior of 100% of those whom He elected to salvation and 0% of the non-elect.  

But the word kosmos in those verses refers to all humans of all time.  

Does that mean that everyone will eventually be saved? 

No.  

Both John 4:42 and 1 John 4:14 show what “Savior of the world” means. 

In his commentary on John 1–6, Hodges wrote concerning John 4:42: 

John concludes his narrative, as well as this unit of his Gospel, with the confession of the men of Sychar. They now believe that Jesus “is indeed the Christ, the Savior of the world.” This confession, of course, expresses the very result that John seeks from this book (see 20:30-31). But it is noteworthy that these non-Jewish believers explicitly express the universal scope of Jesus’ saving power (see 17:2). He is not merely the Savior of His people Israel, but of the entire world. As the Baptist had declared, He is “the Lamb of God who takes away the sin of the world” (1:29)…

What is important is the conviction that the Christ can give eternal life to them, and not simply to Jews. This conviction is emphatically conveyed by the words Savior of the world (Faith in His Name, p. 85, italics his, bolding added).

Concerning 1 John 4:14, I. Howard Marshall says that Savior of the world refers to “the universality of Jesus’ sacrifice” (Epistles of John, p. 220).  Likewise, Gary Derickson says, “This title serves as one of the strong evidences for the doctrine of unlimited atonement (Akin, 183; Johnson, 110). ‘There is no limit to his mission to save, and no limit to its success, excepting man’s unwillingness to accept salvation by believing on the Savior’ (Plummer, 104)” (First, Second, and Third John, p. 453). 

Paul’s words in 1 Tim 4:10 clarify this expression: “For to this end we both labor and suffer reproach, because we trust in the living God, who is the Savior of all men, especially of those who believe.” All men in 1 Tim 4:10 is equivalent to the world in John 4:42 and 1 John 4:14.   

Litfin comments,  

4:10. …Paul stated that God is the Savior of “all men” (cf. 2:2, 4, 6) since He desires that all be saved and He provided Christ as the ransom (2:6) to make that salvation possible. Yet God is the Savior of those who believe in a special way since only in them has His desire for their salvation come to fruition (“1 Timothy” in The Bible Knowledge Commentary, p. 740, italics added).

Similarly, Wiersbe says, “then any lost sinner can trust Christ and be saved” (The Bible Exposition Commentary, p. 227). 

By contrast, some commentators suggest that “Christ is potentially a ransom for the sins of all” (e.g., Lea and Griffin, 1, 2 Timothy and Titus, p. 136, emphasis added). But that is not what Paul said, and it is inconsistent with John 1:29; 4:42; and 1 John 4:14.  

In other words, Jesus, by His death on the cross, made all men savable. So in that sense, He is the Savior of everyone. But He is especially the Savior of those who believe, because they are then saved—given everlasting life.  

Note how radically different that is from the view of many Evangelicals, both Calvinists and non-Calvinists. Most Evangelicals tell the people they evangelize that they are sinners and that their sins separate them from God. They do not say that Jesus has already taken away their sins (John 1:29). They tell people that the shed blood of Christ does not count until you believe that He died on the cross for your personal sins.  

But His blood does count for the sins of the whole world. He has already removed the sin barrier. That is not to say that He has already forgiven all sins. He has not. But forgiveness is not the same as removing the sin barrier.  

Jesus is the Savior of the world. That is wonderful news. People benefit from knowing that they don’t need to deal with their own sins in order to gain eternal life. That’s why repentance is not a condition of everlasting life. Jesus already removed the sin barrier. All anyone must do is believe on the Lord Jesus Christ, and he gains everlasting life that can never be lost (John 1:29; 3:16; 5:24; 6:35, 47; 11:25–27).  

Keep grace in focus and you’ll continue to know that Jesus is the Savior of the world.