Having read all of C. J. Date's book that I could view at the link provided, and having earlier read large portions of several of his other books (and viewed several of his instructional videos), I believe I can pose a useful definition for the phrase in question:
I believe the phrase "logical difference" as use by Chris Date means simply a difference which has logical implications in the context of the subject under discussion, as contrasted with a difference without relevance to the subject under discussion.
This latter type of difference could be called a "superficial difference," but more likely should just be called "irrelevant."
Example: If we are talking about databases, there is a logical difference between the model and the implementation (as discussed at length by Date.)
Example: If we are talking about databases, and I bring up the difference between a computer and a monitor, you wouldn't call this a "logical difference." However, it's not a "superficial difference" either; it's simply entirely irrelevant (inapplicable) to the discussion.
Personally, I would contend that all differences are logical differences.
The relevance or irrelevance of an observed difference to the subject under discussion does not determine whether or not it is a "logical difference," although that is, I believe, an accurate description of how Chris Date uses the term.
The very essence of logic (or sanity) is being able to recognize the difference between two things, and to recognize when there is no difference.
Sanity is the ability to recognize differences, similarities and identities.
(This is a fundamental originally posed by L. Ron Hubbard in 1938.)
Thus the very concept of a "difference" is fundamental to the notion of "logic," so how could it be possible to have a difference that is not a logical difference?
If you replace all usages of the phrase "logical difference" with either "important difference" or "relevant distinction," I do not believe you will lose any meaning.
To borrow Date's own terminology, the concept of "logical difference" is logically the same as the concept of "relevant, important distinction."
By the way, just in case my opinions came across as critical, I want to make it perfectly clear that I think C. J. Date is a genius. :)