Omnichannel is a refinement of the kind of multi-channel approach that I've called content everywhere. Where the content everywhere approach is aimed at delivering content on multiple channels, "Omnichannel is about understanding and optimizing for the entire journey across all channels," as Noz Urbina writes.
To put the point another way: multi-channel provides your users with content across multiple outlets (e.g., your website, social media, an app, etc.). Omnichannel is a strategy for linking those experiences, so that a user's journey is seamless across the entire set of channels.