I agree with Polter. I think it's a lot to do with frequency, intensity, control and why you do it.
People sit tapping their feet and shaking their ankle under their desks, rocking chairs and swinging seats outside are still quite popular (I think). I have friends who always swivel their computer chairs from side to side without really realising they're doing it, and so on and on. Intense emotions often cause stimming. Excited people can hand flap and shocked, frightened or grieving people can rock. It's normal human behaviour.
But there does come a point where I might think 'hmm' if someone described it to me. I mean, to distinguish me from my NT friends and their swivelling chairs and chewed pencil tops, I'm forever making very odd grimacing expressions (every day, usually when I'm excited) without fully realising I'm doing it, properly screwing my face and shoulders up, and I'll often clench a lot of other muscles at the same time, so sometimes I'll find myself with my whole upper body contorted. I rock backwards and forwards every day, but have done it violently enough to accidently smack my head very hard against walls and my bed frame, and break bed slats. I pace (very common in the general population) obsessively for hours a day but suddenly find myself leaping in the air with limbs in an odd position, have smacked lights loose doing that. And that's only the most obvious physical ones, I could make a very long list of things I do. I stim an enormous amount, and it's not JUST an automatic response to emotions, and a stress coping mechanism but I make repetitive movements for hours a day because it's uncomfortable NOT to do so - it's like I can't fully feel my body unless it's in motion and/or muscles are clenched, and then I know where it is. I can't fully control it/suppress it even when I'm not feeling any strong emotions, I can't stop doing it and frankly wouldn't want to.
I don't think, if given a description of all my stims, many people would think that this is 'normal', and tbh many people if (when) they really saw/see me rocking and grimacing, would be/have been incredibly uncomfortable with it because it looks so strange, or even a bit worried/frightened by it.
So basically, to answer, not every autistic person stims an enormous amount, most (nearly all) NT people do it to some extent, but some stims are unusual among NT people, and there's a point on a scale of frequency and intensity where it may well become a sign of an underlying issue - not necessarily ASD, you could have a sensory processing disorder alone, or another neurodevelopmental disorder. The point at which we all think something is unusual and then a sign of an underlying issue, versus noticeable but basically 'normal', will vary somewhat!