In short, no.

(well, if we don't count the kind of significant ability to be freely available for certain purposes)

From https://www.wolfram.com/engine/faq/

How does the Free Wolfram Engine for Developers relate to Mathematica?

It's the same core engine, but with a different interface and different licensing. Mathematica is used primarily for interactive computing, with the Wolfram Notebook interface. The Free Wolfram Engine for Developers is intended to be called by other programs, using a variety of program communication interfaces. The Free Wolfram Engine for Developers is licensed for pre-production use in developing software. Unlike Mathematica, it is not licensed for generating outputs for commercial or organizational use.

"It could be a good idea to also include a link to something like 'Which product serves my needs best?' ":

In a sense WRI already has that information, albeit distributed over a number of pages. What's really lacking is a table comparing features, licensing terms, perhaps even cost.

It's not uncommon when one is trying to pick one of several competing or similar products, or version of a piece of software, to allow the user to check-mark several of the products/versions and then click a button that produces such a table of comparisons.

Is there something more to the interface of Wolfram Engine than is already available with wolframscript + Mathematica?

No, there isn't. In fact, the notebook interface (Frontend) is not available in the Wolfram Engine product.

Can one just as easily — if one had reason to do so! — use a Juypter notebook interface to the kernel of an ordinary Mathematica installation?

Yes, there is nothing special about the kernel found in a Wolfram Engine installation vs a Mathematica installation.

This has been informative, thank you. Just to clarify:

• can the engine produce plots?
• if so, in what format are they returned?

I would like to embed them in (a) in HTML or (b) directly in JavaFX as images.

Is that possible?

Also, my impression is that you cannot invoke Alpha via the engine so that would require a separate, usage-based license, is that correct?

Thanks very much. --larry