I was confused when the author in one case uses the term "detailed design", and in the other "design for construction".
Does he? Well, I searched through the book, and as far as I can see, McConnell nowhere in the whole book uses the term "Design for Construction".
The correct title of chaper 5 is
"Design in Construction"
and in the context of this book about software construction, this makes a IMHO a noteable difference.
To understand what that means, one first has to read chapter 1, where McConnell explains what he means by "Software Construction". There is a nice picture at page 4:
where the grey circle scetches the construction activities in software development. For him, software construction is centered around coding and debugging, but not exclusively formed by those activities.
Now the terms hopefully become clearer:
"Design in Construction" are all the design activities inside the grey circle, which are to a major part belonging to "Detailed Design", maybe also parts of "Construction planning".
A huge part of "Detailed Design" belongs to software construction, but there are also parts outside.
Chapter 5 explains in detail those design activities, and which of them - from McConnells point of view - belong to "software construction". I don't think I can give an adequate summary here in a few sentences, since the chapter is too large for this. So anyone who is interested may get a copy of the book and read the chapter by themselves (disclosure: I have no connection to the publisher or the author).
Let me finally add that McConnell's definition of "Design" is not the only possible or correct one. I recommend to have a look into Jack W. Reeves essays - he makes clear why coding itself is also a design activity and should be called as such, especially when software engineering is compared to other engineering and construction disciplines.