There seems to be a distinction between multichannel and cross-channel, at least in terms of vendor and industry analyst points of view. There is the Magic Quadrant for CRM Multichannel Campaign Management from Gartner and the Trends in Cross-Channel Campaign Management from Forrester. They both talk about a common set of vendors.
There is another possible distinction, that might be useful: publication versus path.
- Multichannel can be thought of in publishing sense - the same, or coordinated, content is distributed simultaneously across appropriate outlets.
- Cross-Channel can be thought of as the sequence of touch points as consumer traverses their path to purchase.