It really is the reproduction and distribution of that material without the approval of the copyright holder or invocation of some kind of approved license, beyond fair use, that would constitute a copyright violation.
Technically it is reproduction OR distribution*. As in, reproducing in and of itself is a violation. Distribution is also a violation. If they are done by separate entities, both can be in trouble.
(*Or public performance. Or broadcasting. Or translation. Or adaptation.)
Copyright simply doesn't view a human experiencing the work as "reproducing" it. So, if someone violates copyright and reprints your book, you are in violation of copyright, but a person who reads that copy isn't in violation.
Copyright law just does not treat the human brain like a computer. And that's a good thing.
Edit to add: Really we should view copyright for what it is - a license. When you purchase media, you are really purchasing the content and a license that allows you to consume it in the normal manner for its type. You have a license to read that book, as many times as you like. You just don't have a license to do anything else with it. And yes, the license is transferrable to anyone in possession of the content covered by copyright.
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