Difference between Discrete Structures and Discrete Mathematics

I remember distinctly that our textbook stated:

Discrete structures are structures that are used in describing discrete mathematics.

Discrete mathematics is math that makes use of discrete structures.

In reality, discrete mathematics is just that, math dealing with discrete values. Discrete structures are somewhat like constructs for discrete mathematics, but also deals with the topic matter. The two, however, as a course name, describe the same thing.

The terms are used so interchangably and are so vague that the people asking you for this likely don't realize what they are asking. I don't think you'll find any resources that give you a clear cut answer, but probably what you want to do is teach discrete mathematics with a focus on the CS perspective.

I have http://www.amazon.com/Discrete-Computational-Structures-Computer-Mathematics/dp/0124208509 which seems to be what they're asking for.

Chapter 1 says "This is a book about structures."

Always, since our interest is in digital computation, our structures will be discrete.

I supposed you could split that hair and say "see, it's just discrete mathematics warmed over." While it might be true, I think it's only a matter of focus.

It becomes discrete structures when the focus is on digital computation.