I would say that the only difference is that MX Key S comes without a Bolt dongle and MX Keys Business comes with a Bolt dongle. So for Logitech, Bolt = Business.

Business Products are more robust than the normal one.

There are a hundred sets with MX keys. I think there are some with illuminated keys and some without illuminated keys. The description also mentions differences in the key mechanism. But the pricing is difficult to understand. Some of the sets are more expensive than the individual devices. Back then, we did it like this: look at the cheapest one and check whether it can do everything you want. And then take it. :-)