I think for the average person these things are synonymous. If you want to cloud stream you pay for a subscription, or at least the way I described it.

Does a subscription service like that exist though?

Anyway yes you could set it up that way, you are correct. But the vast majority of people will not do that, and for me downloading it on a separate piece of hardware kinda ruins the convince aspect I enjoy.

It's kinda like wanting better beef and deciding to raise a cow instead. Like yes that will give you the best quality, but the time investment is much greater. Obviously this analogy is over scaled, so adjust it down a bit. Point is the average consumer isn't going to raise the cow