Nowadays we hear the "display type"/"text type" distinction drawn between different typeface designs more often than between different cuts of the same typeface, I think.
If it looks good large and would be hard to read long texts in, it's a display face. Think headlines or ads.
If it looks good small and would be easier to read long texts in, it's a text face. Think novels or reference books.

There's more (but not much) on the Wiki page.

In my experience, "display type" has meant a distinct member of a type family, such as Minion Display, Miller Display, or Miller Headline. These faces have been made to use with text types, either members of their own families, or with other text faces, specifically at large sizes, as hinted at above. These faces are generally lighter in all ways than text faces. They are often narrower than the text face would be if enlarged to match the visual height of the display face. They usually have a somewhat tighter fit than text faces. And, yes, those nasty ink traps will be gone, but I think ink traps were the least concern in the production of display types that follow the distinctions I just noted.

To see differences between text and display, set the same headline in, say, 60-point Minion Regular and also in 60-point Minion Display. Were you to use that 60-point Minion Regular on a broadside along with text also set in Regular, the headline would be far more powerful than the text. Set that headline in Minion Display and you will get a more elegant relation between text and display. Granted, this is all a matter of taste, intention, and design. If you set the 60-point Regular in a color other than the presumed black of the text, its relation to the text can be more harmonious.

It is too bad, but few faces these days have display weights, and few typographers know how to use them well. We do see them with Miller, Minion, and a few others; to a limited extent the 18 cut of Clifford can be used as a small display face.*

Craig's distinction ("looks good") seems not to take into account the intentions of the typeface designer, and may seem a bit flippant. Craig seems to allow that if a face looks good large but not small then it can be called a display face; and the opposite. In that way "looking good" is generally the result of how a typeface has been used by a compositor or typographer. This way any face well used can be called display. Typeface designers and manufacturers who create a display face and name it " XXX display" have aimed at putting another tool before the typographer. True, where I suggest Craig might have been flippant, I certainly can be called out as pedantic in this case.

There also are some faces called "Titling," such as MT Dante Titling. I think this designation was more common with metal type. "Titling" generally meant all-cap fonts. But it could also imply either differences in the actual forms of some letters or differences in the bodies of the types.

Someone with the old green Monotype binders at his or her desk will have to check me on this. But I recall that in Bembo and Perpetua Titling the J and the Q were different than their text cousins in that the tails of those letters were not drawn as descending strokes. They fit on the body. A 72-point Bembo Q was the same size as the O of the font, tail included; both would be just about 72 points tall. As would the H. Overshoot and undershoot for O and Q, as well as other visual necessities, would have been accounted for in the design.

OR . . . J and Q might have descending parts, but these sorts would be cast on a body larger than the sorts without descenders. In such case non-descending sorts might be cast on a 72-point body, but J and Q might be cast on an 80- or 84-point body. The baseline would be consistent for both body sizes. The hand comp would then fit slugs under the non-d sorts to make a solid line. That was a lot of fun, especially when major changes were later made to such a titling line. This was done to reduce the amout of metal used in production of a face, and was obviously only used for all-cap titling faces.

* One more thing: hot-metal Monotype had some sizes called "small display" faces. Whereas usually the Monotype caster could only cast text type, up to maybe 13- or 14-point, these small display faces, used on the correct keyboard and caster, could be on bodies up to 22- or 24-point. It was slow going for the casting machine, and sometimes some sorts had to be left out of the matrix case. Italic and Roman might no longer live in the same matrix case, and would have to be cast separately, again pieced together by the hand comp. There were only a few faces that had these small display mats; Centaur and Arrighi I recall, as well as Van Dijck and a few others.

& in the end there's nothing wrong with calling faces such as Fry's Ornamented or Koch Antiqua "display" faces, for they could have no other use than as display. But there can be times when these finer distinctions can help us be more precise in describing how typography works and how it looks.

powers

This recently released book might be of interest to you:
Tim Ahrens. Size-specific adjustments to type designs: An investigation of the principles guiding the design of optical sizes
F

I for one welcome your pedantry! :-)

Am I right in thinking that these display/text versions of a typeface only come in by name with the optical (and then digital) printing technology that allows scaling? That is, I know in metal type that different sizes of a typeface usually had different designs accordingly, but there wasn't such a thing as, say, a 16pt Display cut and a different 16pt Text cut of a metal typeface, right? (Where, for example, the former might be used for subheads with a smaller font, the latter as running text in a large-format book.)

I am not aware that there were text and display variants such as you speak of, Craig.

That is, there would not have been 16-pt Centaur Text and 16-pt Centaur Display.

OH, heck; I guess I'm a bit wrong in that assertion. I just thought to look at the types list at Mike Bixler's shop:

http://www.mwbixler.com/specimens.html

See Bembo, Dante, and Perpetua (2 kinds of titling, 4 sizes with text, light titling, and titling), Poliphilus. & Albertus is an strange anomaly.

It is too bad he does not have showings for all the faces. They'd reveal the diffs between text and titling.

powers

Very interesting!

Back into the future, what kind of typeface is a display typeface?
Is it Arno Display? is it Sugar Pie from SudTipos? are *grabs a shield* the myriad of ornamental fonts in DaFont, 1001fonts resembling everything from organic shapes, japanese kanjis, to LCD displays? (and let's better not forget about grunge fonts).
Is it the optical adjustment? is it what we use it for?
If it is what we use it for then any typeface is prone to be called Display. Now, most of the fonts that are currently called Display (and the name is not due to an optical adjustment) like Alpine Script, would have been called Ornamental if they were issued a decade earlier. But so are grunge fonts, but I don't think many people would call them Display fonts. So, after the optical adjustment and proper size for headlines (some say the Display size is a bit more compressed to fit the larger size in the limited space of a headline but that's a lie, check the new Marzo font from SudTipos), is the Display name an elitist label?
In the end there appears to be two Display terms in typography: the optical and size and a refined stylistic set of a style once known as Ornamental?

Well, hell. The last 20 years or so has seen a great deal of change and fluidity in typo-terminology. So I say you can call it what you want to call it.

You can use the older, more formal term "Display" to denote familial cuts of a face. Or you can use the word "display" to refer to any type used in any of several ways: set large, set to draw attention, etc.

The thing is: if you are going to use the term, make sure you are very clear about what you mean. In any evolving jargon or argot a term can have several meanings. It behooves us to be very clear about how we use the word. "Display" or "kern" may mean one thing to typographer A, and another thing to compositor B. Each must be clear about it to avoid confusion.

powers

P.S.: Nothing written above was a "lie". Less than 100% accurate, perhaps, but not a "lie."

yeah, I just jot "lie", inaccurate is a better term.
Maybe they should be called Ornamental again in order to separate the form from the adjustments of dimensions.

A "display typeface" is a simply a typeface meant to be used larger than text sizes, whether it's part of a family that includes text sizes or not. In fact, the vast majority of display typefaces do not have corresponding family members meant for text sizes. (And vice versa, it could be argued.)