But calvinistic theology does not "say different."
It gladly agrees that whoever believes in the only-begotten Son of God should not perish but have everlasting life.
However, John has already those who believe, in John 1.12-13 saying:
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But as many as received Him, to them He gave the right to become children of God, to those who believe in His name:
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who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
They see belief as a gift from God, as stated, for instance, in Philippians 1.29:
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For to you it has been granted on behalf of Christ, not only to believe in Him, but also to suffer for His sake.