While both applications are very similar, they are still evolving and more functionality will be added over time.
ArcGIS Explorer Online is meant to be more of a data exploration and viewing tool. For example, there is a new feature called Dashboard that allows you to compare the attributes of different features on the map and graph them. Explorer Online also introduced Presentations, and it's still the app you use to author them, but people asked to be able to display these from the ArcGIS.com map viewer too, so we added support for them. Explorer Online also requires the Microsoft Silverlight plugin in order to run. This can be a stumbling block for some people. Explorer Online is map focused. It doesn't allow you to manage other kinds of items you upload to ArcGIS Online.
ArcGIS.com has a lot more tools for managing your content. You can upload different types of data, such as packages, and desktop files like MXDs and LYRs.
In reality, these are just two of the client applications that can connect to ArcGIS Online. We also have an iPhone application, Android application, ArcGIS Desktop, and have a few different APIs that allow you to develop your own applications that use content in ArcGIS Online.
Hope this helps,
Mike
