SharePoint Online is the SharePoint in Cloud in Office 365, this version is released after SharePoint 2013. SharePoint 2016 Hybrid is expected to release next year (in 2016) which is the new version after SharePoint Online.
Today I tried to migrate SharePoint Online data from my First Office 365 account to another SharePoint Online on Second Office 365 account. So lets name it as:
- SP 001 (Source SharePoint Environment)
- SP 002 (Destination SharePoint Environment)
I used this free tool and found it really useful, the great thing about this tool is that it is free and you can migrate upto 25GB of Data. Software Link -> http://www.metalogix.com/Resources/Promotions/Content-Matrix/Content-Matrix-Migration-Express-Download.aspx
The only thing that would need customization is the look and feel of the home page of the Destination Office 365 account, as the source site will migrate as a Subsite to the Destination SharePoint Online account.
Users Permissions and Domain account would also need revision, if any workflow is attached with a user account (SP 001 account), then you would need to change the permissions with the new user account on SP 002 domain.