“Now Faith.” Faith in the word of God is specially of three sorts: historical, miraculous, [and] justifying or saving faith.
First, historical faith is not only a knowledge of the word, but an assent of the heart to the truth of it. And this faith is general not only to all men, good and bad, but even to the devils themselves: “Thou believest there is one God, thou doest well: the devils also believe it, and tremble” (James 2:19), Now he that will believe out of the Scripture there is one God, he will believe historically anything in the Scriptures.
Second, miraculous, or the faith of miracles, which is an inward persuasion of the heart wrought by some special instinct of the Holy Ghost in some man, whereby he is truly persuaded that God will use him as His instrument for the working of some miracles. This is also general, both to elect and reprobate. Judas had it with the rest of the apostles.
Thirdly, (commonly called justifying) faith, which is a special persuasion wrought by the Holy Ghost in the heart of the those that are effectually called concerning their reconciliation and salvation by Christ.
Of these three sorts sof faith, the third is principally meant in this place….
William Perkins, Comentary on Hebrews 11 The Works of William Perkins, vol. 3. ed. Randall J. Pederson and Ryan M. Hurd (Grand Rapids: Reformation Heritage Books, 2017), 6.
Would you see Perkins even saying that the faith in –
 By faith the people crossed the Red Sea as on dry land, but the Egyptians, when they attempted to do the same, were drowned. (ESV) –
Is justifying faith?
See pp. 315–24 of volume 3.
The First Type of Faith, the Historical, would describe the Sandemanians, the modern
“Free Grace” movement & many antinomians would it not, and even those Faith + works
types of Christianity were the faith need be nothing but bare mental assent, just as rome demands, as “Rabi” Duncan said once that Sandemanianism was “the doctrine of justifying righteousness along with the Popish doctrine of faith.”