Here is Martin Luther’s discussion of the difference between hope and faith from his Galatians 5:5 commentary. (Thanks to Pastor Bryan Wolfmueller for this gem.)
Therefore faith and hope differ first in their subjects:
because faith is in the intellect and hope is in the will; yet they cannot be separated in fact, just as the two cherubim of the mercy seat cannot be separated (Ex. 25:19).
In the second place, they differ in their function:
for faith commands and directs the intellect, though not apart from the will, and teaches what must be believed. Therefore faith is teaching or knowledge. Hope is exhortation, because it arouses the mind to be brave and resolute, so that it dares, endures, and lasts in the midst of evils and looks for better things.
Furthermore, faith is a theologian and a judge, battling against errors and heresies, and judging spirits and doctrines. On the other hand, hope is a captain, battling against feelings such as tribulation, the cross, impatience, sadness, faintheartedness, despair, and blasphemy; and it battles with joy and courage, etc., in opposition to those great evils.
Finally, they differ in their objects:
as its object faith has truth, and it teaches us to cling to this surely and firmly; it looks to the word of the object, that is, to the promise. Hope has goodness as its object; and it looks to the object of the word, that is, to the thing promised or the things to be hoped for, which faith has ordered us to accept. (Luther’s Works 27:22-23)
“For everything that was written in the past was written to teach us, so that through the endurance taught in the Scriptures and the encouragement they provide we might have hope.” (Romans 15:4)