It seems that suffering is the more general term, if only because any harm that someone undergoes is suffered by them. Is there anything that we suffer that is not a harm? I didn't win the sprint, and that didn't harm me exactly, but I did suffer a loss. Is that right? If so, can we suffer because of death even if we are not harmed by it, as e.g. Epicureans I guess claim? I cannot read this article
I may be missing a nuance, but if harm is something externally imposed on someone that creates suffering, then the entire class of mental disorders qualifies as suffering without harm. Being depressed or bipolar involve great suffering, yet there is not harm to point to.
We also suffer because of death insofar as it cause distress to the living or ends an otherwise happy life with more happiness expected in the future.