What does Reformed theology teach about the extent of Christ’s atonement? Francis Turretin (d. 1687) explained definite atonement well:
“The common opinion of the Reformed is that Christ – from the mere good pleasure of the Father – was appointed and given as a Redeemer and head, not to all men, but to a certain number of men. By the election of God, these compose his mystical body. For these alone, Christ, in order to fulfill the decree of election and the counsel of his Father, was willing and determined to die, and also to add to the infinite price of his death a most efficacious and special intention to substitute himself in their place and to acquire faith and salvation for them.”
Turretin then went on to mention the texts in Scripture that talk about Christ’s death being for “his people,” “his sheep,” “his friends,” “his church,” and “his body” (Mt. 1:21, Eph 5:23, Jn 10:15, Jn 15:13, etc.). Turretin also noted how the acquisition and application of redemption are inseparable from the extent of it. In other words, Jesus redeemed his people and applied redemption to the same ones, his elect.
“It is gratuitous [unwarranted] to say that Christ is the Savior of those for whom salvation is indeed acquired, but to whom it will never be applied. Even the very word ‘to save’ denotes the actual communication of salvation, and Christ is Jesus, not only because he is willing and able to save and because he removes all obstacles out of the way of salvation, but because he does really and actually save his people, not only by his merit acquiring salvation for them, but also efficaciously applying it to them, which was the intent of God in sending Christ and the end of his mission (as the angel clearly intimates by the imposition of the name ‘Jesus’).
Jesus is not possibly a Savior; he’s not a potential Redeemer. He actually saves and is a true Redeemer!
The above quotes are found in volume 2 of Turretin’s Institutes of Elenctic Theology, 458 & 461.