On Sunday, August 11, 2019 at 12:49:21 PM UTC-7, Tom Kunich wrote:
The only difference between the 5-6 and the 7-8 and 9 speed chains is the distance that the rivets stick out if memory serves. Also they are far more flexible since high-high and low-low are so wide apart.

I think technically, 5-6 pin chains had pins (not rivets) that were simple cylinders. With 8 speed chains, there's so little protrusion that the plates couldn't be trusted to stay on a simple cylinder, so pins are swaged (riveted) for retention. I'm not sure which way things went for 7 speed, though it may be that different manufacturers went different ways for that.

There's also differences in construction and plate shape.

5/6 speed chains were originally bushing chains. Then Sedisport came along with a narrow bushingless chain for ultra-6/7. I think there was some overlap in this era, with SunTour favouring stiffer chains for Accushift while Shimano went to more flexible bushingless chains for SIS. AFAIK everything since then has been bushingless.

The other thing is side plate shape. In the 5/6 speed days, Shimano Uniglide chains had bulging outer plates to better snag adjacent sprockets for shifts. The earliest ones were too wide to fit the 5.0mm sprocket spacing of 7-speed, so there were so-called narrow chains, which presumably had less of a bulge.
Subsequent chains got narrower and narrower (making the 'narrow' designation of 7-speed kinda backwards nowadays) with the plates bulging less and less. I think 10-speed chains have gone back to being completely flat, but even before that, I think (but am not sure) 9-speed chains went to thinner side plates.