Hi,
According to your description, my understanding is that you want to know about integration CRM with SharePoint online and the difference between integration CRM between SharePoint 2013 on-promise and online.
It is possible integrate CRM on-promise with SharePoint online.
With Microsoft Dynamics CRM, you can use the document management capabilities of Microsoft SharePoint from within Dynamics CRM. You can store and manage documents in the context of a Dynamics CRM record on a SharePoint Server, and leverage the SharePoint
infrastructure to share, manage, and collaborate efficiently.
About setting up SharePoint integration with Microsoft Dynamics CRM for your reference:
https://technet.microsoft.com/en-us/library/Dn531154.aspx?f=255&MSPPError=-2147217396
There are 2 ways of integrating SharePoint with Dynamics CRM: Client-to-server integration and Server-to-server integration. The client-to server integration is supported for both online and on-premises versions of CRM and SharePoint. The server-based integration
is supported for SharePoint Online, and SharePoint on-premises only if you have Microsoft Dynamics CRM Online 2015 Update 1.
More information about the two ways for your reference:
https://msdn.microsoft.com/en-us/library/gg334768.aspx?f=255&MSPPError=-2147217396
http://community.aiim.org/blogs/amila-hendahewa/2015/03/14/integrating-microsoft-dynamics-crm-with-sharepoint
Thanks,
Dean Wang