Pain and distress differ, but overlap. For the purposes of this discussion, we will consider pain to involve nociceptive input of stimuli that are potentially tissue damaging, and that further include an unpleasant emotional component (Merskey and Bogduk 1994). Pain need not necessarily induce distress, as when an animal or human willingly undergoes some painful situation in order to achieve a desired reward. In that case, while the pain may be unpleasant, it is not so severe as to be intolerable. Likewise, there are many potential causes of distress that do not involve physical pain.
Carbone, Larry, "Measurement and Mitigation of Laboratory Animal Distress Sources of Distress in the Animal Laboratory" (2009). Laboratory Animals. Paper 21.