Share is mostly ,eh, for sharing. You provide others a location to view maps on-lline (with some limitations) and/or download them to be opened in the desktop version. You can control whether the maps there are public or not (for you only, for all who know where to look, or for really anyone).
Cloud is more to yourself, a location to store so that you can continue to work on your map on another computer (desktop version of Xmind) or with a web-browser (any device with a web-browser). It also allows you to show your work to others using just a browser.
Neither cloud solution support collaboration, at least in any feasible way, in any level.
More a personal opinion...
Share is rather superfluous. There are more than enough sharing services, and many users probably use already some of them (Dropbox, iCloud, Google Docs etc.) so the only things Share brings on the table are the ease of sharing (directly in Xmind) and a public gallery of maps (if you decide to publish your map to all).
Cloud is for those who have cried for a version of Xmind for iPhone/Android/whatever-mobile-device. Instead of investing a device-specific versions of Xmind, the company has made a version that can be used with just a web-browser. I fail to see any real use of Xmind Cloud on a mobile device but the ability to show maps with just a browser might come handy one day.