Cross-channel offers a different stance from both multi-channel and cross-media: the single channel might or might not offer a complete entry point into the ecosystem, but the fact is that most of the users / customers will not stay in that channel from point A to point Z. In other words, it might very well be that in a ubiquitous ecology some channels do allow users to complete their experiential journey without resorting to other channels, in contrast to cross-media, but that is not going to happen very often (or at all, in contrast to multi-channel). This is where the specific nature of cross-channel lies, and where the challenges for design reside.
-What is Cross Channel

Some hair splitting thoughts on wrangle multi-touchpoint experiences from an Information Architecture perspective. Im not sure I agree with or understand the points fully, but the idea of a task arching across multiple channels is certainly an interesting design challenge for multi-touchpoint experiences. The description of multi channel experiences uses concrete examples, while the description of cross channel devolves into ambiguity. It does make me want to read the book.