You absolutely can exercise without being sore. If you head over to /fitness on that other social media site there are plenty of people who can vouch for the fact that doing some decent lifting can end up in a spot where soreness doesn’t happen. I’ve been there, and it kinda sucks because that soreness is sort of a mental reward that “heck yeah, I did work today” and when it’s gone you miss it.
I think people are smart enough to know the difference between not working out and still sore/having pains, temporary exertion and hurting oneself causing soreness/pain,and workout soreness.
I’m not sure that pursuing the semantics of the words and subjective feelings of the differences between soreness and pain is worth pursuing here.