Roughly, pain is a sensation typically associated with damage to the body, suffering is an experience of stimuli as intrinsically unpleasant.
I do not suffer if my room is painted a color I do not like, but I still may care about the color my room is painted.
Yeah, that’s certainly a fair clarification. It’d probably take a lot more space to give a really robust definition of “suffering”, but that’s close enough for gummint work.