It would be really useful to have a comparison page on the Wolfram site that lists Wolfram|One and Mathematica, the same way that I can compare a macBook Pro and an iMac on the Apple website.
Other than the fact that Wolfram|One is subscription only, I can see no difference in the products.
I notice that Stephen Wolfram seems to use Wolfram Desktop a lot in his presentations when he is talking about Mathematica, so as far as desktop functionality is concerned, there cannot be any difference.
When Wolfram|One was first released, I thought that it was a simple rebranding of Mathematica. After all, Mathematica has expanded well beyond its original purpose -- "A system for Doing Mathematics by Computer", as the subtitle of the original Mathematica book states. Whether or not it would make marketing sense to unify the products under the new name is problematic. As a long-time user since version 1, I would have no problem with the renaming, but almost 30 years of mostly free publicity is hard to give up.
What I find odd is that various Wolfram Research offerings do not play well together. For example, my premier service plus plan for Mathematica does not give me access to the Wolfram Programming Lab or the Wolfram Development platform, even though I already have all the functionality. (Some of the UI features of the Programming lab are useful when trying to teach newbies, for example.)
I prefer to 'own' the software, rather than renting it, and the latter seems to be the only option for Wolfram|One. For a professional user, one is paying a yearly fee of about half the outright purchase price for Mathematica, so if one is using the program more than two or three years, it is less expensive to buy Mathematica and purchase Premier Service every year than to continue with an annual fee. I see that there is an annual subscription for Mathematica, which is almost exactly the same price as the subscription for Wolfram|One.
I did a quick check of the pricing for the home use/personal use, and the benefits are exactly the same. The subscription price is exactly the same as well. So, you can pay a bit more to buy Mathematica initially, and have a lower annual cost for each subsequent year, or rent the software. I hadn't looked at this pricing before because I have an Industry license, and there are more options with this.
So, the real question remains: what is special about Wolfram|One, compared to Mathematica? If you use the subscription model for Mathematica, I can see no difference between the two. The advantage of Mathematica for me is that the yearly cost of ownership is substantially less with the outright purchase of Mathematica plus Premier Service Plus, and would be for a new user as well.
I did talk about this matter with my account manager when Wolfram|One was released, and he could not find any difference in the products, other than the licensing model. However, he was probably looking only at the Industry license (which I have), and not at the other user categories.
To conclude, as far as I can tell, the only difference between Wolfram|One and Mathematica, other than the name, is the fact that Wolfram|One is available only as an annual subscription, while Mathematica can also be purchased outright. With the current pricing schemes, the only relevant consequence of this is that the cost of 'ownership' is significantly less for Mathematica (purchase plus Premier Service Plus) if the program is kept up-to-date for more than two years. (This break-even point may vary a bit by user-type, but it is close enough.)
The one remaining nagging detail that the marketing pages do not cover is the explicit statement that all the features and functionality of the Wolfram Language are equally supported. This is of concern because other Wolfram Research products: Data Science Platform, Finance Platform, and System Modeler differentiate themselves by offering additional functionality not provided with Mathematica, and presumedly, Wolfram|One. So, if there really is extra functionality in Wolfram|One that is not made explicit on the marketing pages, it would be useful to know that.
I think that this is the thrust of this thread.