In the past, there have been some major differences between SharePoint Online and SharePoint On Premise. For one, SharePoint Online used to trail the version of SharePoint that was available On Premise. For example, when SharePoint 2010 came out, it took SharePoint Online a painfully long time before it became SharePoint 2010.
The current version is SharePoint 2013. The previous version was SharePoint 2010, and the version before that was SharePoint 2007. SharePoint Online doesn’t have a version number.
Times have changed, and Microsoft has said it’s moving toward feature and release parity, meaning that SharePoint Online will be the equivalent of SharePoint On Premise, and both will be SharePoint 2013. The only difference will be in how you access it. In addition, the functionality available in SharePoint will also be nearly identical between SharePoint On Premise and SharePoint Online.
With that said, there are still integration points and advanced functionality that are only available with SharePoint On Premise. This is an ever-changing landscape, so the best way to stay on top of the available features is on the frequently updated SharePoint Online feature matrix located on Microsoft’s TechNet website.
SharePoint Online is when Microsoft manages SharePoint in their data centers and you access it over the Internet. SharePoint On Premise is when your local IT gurus manage SharePoint in your company data center.