Objection 1. It would seem that sorrow is not pain. For Augustine says (De Civ. Dei xiv, 7) that "pain is used to express bodily suffering." But sorrow is used more in reference to the soul. Therefore sorrow is not pain.
Objection 2. Further, pain is only in respect of present evil. But sorrow can refer to both past and future evil: thus repentance is sorrow for the past, and anxiety for the future. Therefore sorrow is quite different from pain.
Objection 3. Further, pain seems not to follow save from the sense of touch. But sorrow can arise from all the senses. Therefore sorrow is not pain, and extends to more objects.
On the contrary, The Apostle says (Romans 9:2): "I have great sorrow [Douay: 'sadness'] and continual pain [Douay: 'sorrow'] in my heart," thus denoting the same thing by sorrow and pain.
I answer that, Pleasure and pain can arise from a twofold apprehension, namely, from the apprehension of an exterior sense; and from the interior apprehension of the intellect or of the imagination. Now the interior apprehension extends to more objects than the exterior apprehension: because whatever things come under the exterior apprehension, come under the interior, but not conversely. Consequently that pleasure alone which is caused by an interior apprehension is called joy, as stated above (Question 31, Article 3): and in like manner that pain alone which is caused by an interior apprehension, is called sorrow. And just as that pleasure which is caused by an exterior apprehension, is called pleasure but not joy; so too that pain which is caused by an exterior apprehension, is called pain indeed but not sorrow. Accordingly sorrow is a species of pain, as joy is a species of pleasure.
Reply to Objection 1. Augustine is speaking there of the use of the word: because "pain" is more generally used in reference to bodily pains, which are better known, than in reference to spiritual pains.
Reply to Objection 2. External sense perceives only what is present; but the interior cognitive power can perceive the present, past and future. Consequently sorrow can regard present, past and future: whereas bodily pain, which follows apprehension of the external sense, can only regard something present.
Reply to Objection 3. The sensibles of touch are painful, not only in so far as they are disproportionate to the apprehensive power, but also in so far as they are contrary to nature: whereas the objects of the other senses can indeed be disproportionate to the apprehensive power, but they are not contrary to nature, save as they are subordinate to the sensibles of touch. Consequently man alone, who is a perfectly cognizant animal, takes pleasure in the objects of the other senses for their own sake; whereas other animals take no pleasure in them save as referable to the sensibles of touch, as stated in Ethic. iii, 10. Accordingly, in referring to the objects of the other senses, we do not speak of pain in so far as it is contrary to natural pleasure: but rather of sorrow, which is contrary to joy. So then if pain be taken as denoting bodily pain, which is its more usual meaning, then it is contrasted with sorrow, according to the distinction of interior and exterior apprehension; although, on the part of the objects, pleasure extends further than does bodily pain. But if pain be taken in a wide sense, then it is the genus of sorrow, as stated above.
Source: Summa Theologica (New Advent)