The phrase, appropriating faith, does not indicate a faith, which is different in its kind or nature from any other faith. Faith, in its nature, is always the same. It indicates a form or modification of faith, however, which should not be confounded with other forms.
Appropriating faith is a faith, which considers the object of faith, the thing believed in, whatever it may be, in its relation to ourselves.
But in order more fully to understand this statement, perhaps we should say here, that there are three distinct modifications of faith, which may properly be noticed, in connection with each other, viz.: historical faith, a general religious faith, and that more specific or appropriating faith, which we have at present under consideration.
— edited from The Life of Faith (1852) Part 1, Chapter 10.