Printers deal in inches while typesetters deal in picas and points; or so we used to tell ourselves in the days when there actually were things called typesetters. The trade still survives but travels under names like text processing, composition, editorial services. So in speccing the book you’d tell the typesetter to leave say 1 pica and 6 points, or 18 points, space above the chapter title. You wouldn’t tell them to leave ¼” even though that would have come to the same distance — the inch containing 72 points (approximately, but close enough for the difference to be irrelevant. Actually, nowadays the point is exactly 1/72″, since Apple decided it should be so when they introduced the Mac.) Your line length, interlinear spacing, indentation for tables or whatever, would all be expressed in points (or picas and points). The only inch measurement you’d give the typesetter would be the trim size, and the width of the gutter and head margins (these being ultimately measurements directed at the printer). The typesetter didn’t really need to know these inch measurements in the sixties and seventies: what they produced back then — a page of type — would look the same wherever the designer fancied it would fit onto the page, but we did provide the information to them.* (Now of course with press-ready files going direct to the printer, this information is again required.)
You couldn’t (or shouldn’t) tell the printer to sink chapter openers by 1 pica and 6 points. Even telling the printer to sink chapter openers by ¼” would have been risky. The stripping department (like any other) would tend to be working at full speed, and a niggly written instruction like that would be likely to get overlooked. In the example illustrated I’ve drawn in the corner marks we’d add in such cases so as to prevent the overzealous stripper from hanging everything from the top, which was their default mode. Doing this would obviously pull the bottom of the page up by ¼” preventing it from aligning with other drop folios. Sometimes we would indeed add corner marks by hand as in this example, but most often the typesetter would insert them as part of their routine for setting a chapter opener. After the pages had been stripped up the stripper was meant to opaque out these corner ticks, usually by covering them with a bit of the dark red tape they’d use to attach the single-page negs to the goldenrod. (See Flats.) Naturally there are in existence one or two books where you can see some of these ticks which got overlooked and were never opaqued or taped out. Several film setting systems also provided center marks at top and bottom and at the sides: these too you can occasionally find sneakily printing.
Why do typesetters deal in points? The inch is just too big to be useful. In the beginning printers and type founders tended to use their own systems of measurement, and this chaos worked fine as long as the industry remained small and there was no interaction between different plants. Efficiency would demand standardization in order to bring down the cost of making equipment and in the nineteenth century we settled down. The revolutionary French were in the vanguard in this. About 1783 François-Ambroise Didot introduced his system based upon Pierre Simon Fournier’s earlier version. Didot based his system on the pouce, the French royal inch. One Didot point measures 0.3759715104mm, usually rounded off to 0.0376mm. A Cicero is the French equivalent of our pica, 12 Didot points.) An American point measures 0.35136666 mm. The difference is explained by the fact that the official standard approved by the Type Founders Association of the United States in 1886 was the Johnson pica, equal to exactly 0.166 inch. Maybe they chose this standard for sentimental reasons, since its ancestry went back to the press which Benjamin Franklin had bought from Fournier while he was in France. Such minuscule differences don’t seem to have caused any difficulties: the direct communication between French and British or American printers was minimal — at least until the offset and now digital eras. The British industry followed the Americans, making the formal decision in 1903. No doubt this would be because Monotype and Linotype machines originated in USA.
The most intriguing measurement your American publisher will get to deal with is the carload. This is the amount of paper that could be fitted into some notional railway car at some point in time, now clocking in at 44,000lbs, or 43,000lbs, or 42,000lbs depending on the mill doing the counting, and is a regular price-break point in paper sales. No doubt it originated from the freight rate pricing of rail companies at a time when all freight went thataway.
* That we gave it to them was a survival from letterpress days. After the hot metal type had been set into galley and proofed, the composition room would need to make it up into pages and then impose those pages into formes. Obviously at that point information about positioning on the page would become essential.