Objection 1. It would seem that hope is the same as desire or cupidity. Because hope is reckoned as one of the four principal passions. But Augustine in setting down the four principal passions puts cupidity in the place of hope (De Civ. Dei xiv, 3,7). Therefore hope is the same as cupidity or desire.
Objection 2. Further, passions differ according to their objects. But the object of hope is the same as the object of cupidity or desire, viz. the future good. Therefore hope is the same as cupidity or desire.
Objection 3. If it be said that hope, in addition to desire, denotes the possibility of obtaining the future good; on the contrary, whatever is accidental to the object does not make a different species of passion. But possibility of acquisition is accidental to a future good, which is the object of cupidity or desire, and of hope. Therefore hope does not differ specifically from desire or cupidity.
On the contrary, To different powers belong different species of passions. But hope is in the irascible power; whereas desire or cupidity is in the concupiscible. Therefore hope differs specifically from desire or cupidity.
I answer that, The species of a passion is taken from the object. Now, in the object of hope, we may note four conditions. First, that it is something good; since, properly speaking, hope regards only the good; in this respect, hope differs from fear, which regards evil. Secondly, that it is future; for hope does not regard that which is present and already possessed: in this respect, hope differs from joy which regards a present good. Thirdly, that it must be something arduous and difficult to obtain, for we do not speak of any one hoping for trifles, which are in one's power to have at any time: in this respect, hope differs from desire or cupidity, which regards the future good absolutely: wherefore it belongs to the concupiscible, while hope belongs to the irascible faculty. Fourthly, that this difficult thing is something possible to obtain: for one does not hope for that which one cannot get at all: and, in this respect, hope differs from despair. It is therefore evident that hope differs from desire, as the irascible passions differ from the concupiscible. For this reason, moreover, hope presupposes desire: just as all irascible passions presuppose the passions of the concupiscible faculty, as stated above (Question 25, Article 1).
Reply to Objection 1. Augustine mentions desire instead of hope, because each regards future good; and because the good which is not arduous is reckoned as nothing: thus implying that desire seems to tend chiefly to the arduous good, to which hope tends likewise.
Reply to Objection 1. The object of hope is the future good considered, not absolutely, but as arduous and difficult of attainment, as stated above.
Reply to Objection 3. The object of hope adds not only possibility to the object of desire, but also difficulty: and this makes hope belong to another power, viz. the irascible, which regards something difficult, as stated in the I, 81, 2. Moreover, possibility and impossibility are not altogether accidental to the object of the appetitive power: because the appetite is a principle of movement; and nothing is moved to anything except under the aspect of being possible; for no one is moved to that which he reckons impossible to get. Consequently hope differs from despair according to the difference of possible and impossible.
Source: Summa Theologica (New Advent)