You should only have one EndNote Library. Multiple libraries inevitably means confusion with where references are saved, duplication and mistakes. However, you can have the same EndNote Library available on more than one device, and to do this, you need to 'sync' your EndNote 21 (desktop) Library with EndNote 21 (online). Syncing with EndNote 21 (online) also:
If you have previously used EndNote Online/Basic and wish to start using EndNote Desktop, syncing will get all of your online library references into your new desktop library.
If you wish to sync your accounts, you do this within EndNote desktop. See instructions at: