The characteristics of the Modern (Didone) style are:

High contrast
Vertical stress
Unbracketed serifs

The class of Scotch types meets the first two criteria, but its adherence to the third varies.

The Scotch has bracketed serifs.

There are two ways of looking at this--strictly taxonomic (i.e. what the physical features are), or philogenic (how they evolved).

So we have the Panose system, with

cove
obtuse cove
obtuse square cove
square cove
square

which are taxonomic

and IBM with

transitional
modern (didone)
clarendon
slab

**

Some wrinkles:

The Century styles are Scotch, but in headline faces they tend towards modern, and in text, towards slab.
Times Roman has Scotch capitals, but not lower case--except in the bold. Bit of a mash-up.
Press gain on letterpress text gives the impression of subtle bracketing.

When Richard Austin, inventor of the Scotch, started his own foundry, he addressed the problem of easily damaged type by coming up with what I term the Scotch Modern -- the style with huge, fine serifs and tiny aperture. The brackets are so attentuated that they thin out, becoming didone-like. It was that style of type which was first termed "modern" in the late 19th century, not Bodoni, which had yet to be revived, and which is probably now considered most typically "modern".

So, as the distinction between Modern and Scotch rests on the degree of bracketing, the degree of "Scotchness" of a particular typeface may vary with both its optical size, and the foundry that produced it.

For instance, consider these four faces. Pretty similar, eh?
Yet De Vinne is generally considered a Modern, Georgia and Century Scotch, and Clarendon a slab serif.

And does neoclassical cover these styles and stop at slab? Good thread, good explanation.

Yeah, thanks for this thread and the explanation.

Interesting… so then it's all about the bracket?

Would that make Monotype Modern technically not a strict Modern but a Scotch Modern?

It's funny because over time, my hyper-simplified technique was to just look at the cap R, and depending on the upstroke at the end of its leg, I would make my distinction. Anything with an extreme flip (à la De Vinne) I labeled as Scotch and reserved Modern for the earlier French originals. I think perhaps my assumption of what was typically Scotch was what you refer to more as Scotch Modern… those exaggerated Austin-esque versions which just scream Victorian. For whatever reason, I was lumping those faces in with the sturdier, less exaggerated Scotches like Miller.

Perhaps my scale should look something more this this:
|Didone----|--Modern--|--Scotch Modern--|----Scotch|

?

Is it appropriate to separate Didone from Modern?

I'd also be curious to know where you would place something like Zooth (for lack of a better example) – the Moderns with ridiculously large (but still unbracketed) serifs.

Would that make Monotype Modern technically not a strict Modern but a Scotch Modern?

That's my view, and I do think the nature of the Scotch is open to interpretation.
19th century typography generally hasn't been given critical respect or attention, so there is still much to be discussed and theorized.

Hoefler & Frere-Jones, in the blurb for their Chronicle, consider the Scotch to be Transitional.

What then does that make typefaces like Century or De Vinne, with their enormous serifs and pot-hooks on a and R?
They're not modern, in the sense that they don't have the Modern's openness and reductive simplicity.
Aesthetically, they are between Oldstyle and Modern, but they are not transitional, as we understand that as meaning "on the way to".
They follow on from the first Modern types of Didot and Bodoni, but we can't call them Post-Modern -- too 20th century.
So that's why I've suggested Scotch Modern as a term for this genre.

Interesting read. Thanks, Nick!