EndNote Online is both a web-based version of EndNote (with fewer features) and a method for accessing and sharing EndNote libraries created and managed with the full version of EndNote.
EndNote Basic - EndNote Online only. "Perfect for the new-to-research and writing student." Direct Export and Cite While You Write work, but EndNote Basic stores fewer references and PDfs, and offers fewer output styles.
EndNote Desktop - EndNote calls this version "EndNote Online With the Desktop." All the features of EndNote Basic, plus find full text, search and annotate PDFs, and create new output styles. Compare EndNote Basic and EndNote Online With the Desktop.
EndNote Sync - Sync desktop and online libraries. Also share an EndNote library or group by syncing with up to 14 other EndNote users.
UVM offers EndNote Desktop, which includes the features of EndNote Online and EndNote Sync.
EndNote Library Syncing and Sharing (text and video) - scroll down to see how to sync libraries.