If you sign up for the Office 2013 Preview, you will notice the product is also referred to as Office 365.
The branding and nomenclature can feel a tad unclear.
Luckily, perspective on these products comes into focus when you consider a few key ideas.
Microsoft's Marketing Challenge: Get Desktop Users to Adopt Office 365
It does seem that Microsoft is at times using these two different product names interchangeably in an effort to lead consumers to switch from desktop versions of Microsoft Office (Office 2003, Office 2007, Office 2010, and now Office 2013, for example) to the latest, cloud-based Office 365.
The blended approach is also due to product evolution. The lite versions of program apps previously available under the name 'Microsoft 365' have now grown into full versions of these programs: Office 2013 Office 2013. They represent a made-over part of Office 365.
Microsoft is definitely trying to get users to adopt Office 365, as evidenced by the Time to 365 campaign. The future will likely bring more along these lines. Interestingly, Office 365 may be a required subscription for accessing editing functions in the Microsoft Office Apps for Android and iOS expected in Early 2013.
The Greater Context of Cloud-based Environments in General
Cloud computing adds a new layer to how we think about computer organization. It can be thought of as adding a new drive one can save to, but is actually more than that. Entire computing functions can also be hosted in the cloud, which goes way beyond thinking of this as an extra storage unit in the sky. In that sense, cloud computing is more like a community of virtual computing that you can opt into.
In fact, Microsoft has emphasized its increasingly ecosystem-oriented approach to productivity along with Office 2013. That's why the timing on this is all swept up in one jumble of names--which may seem to signify different things at one time, but at another time they are used almost synonymously!
Check out Office 365 University
Some of SkyDrive's Moving Parts
The nitty-gritty of this relationship goes like this...SkyDrive is the entire Microsoft cloud. Office 365 is the portion of that cloud for all productivity solutions, one of which is the new Office 2013 suite (the Word, Excel, PowerPoint, Access, Publisher, Outlook, and OneNote software bundle).
The Role of Time in This Name Game
The names can feel particularly misleading because the apps and services previously known as Office 365 are only one part of what you will get with new Office 365 Subscriptions.
If you can suspend the need for exact nomenclature, that is probably your best strategy here. Knowing that the products are distinct, yet very overlapping, will help you cringe less when you see 'Microsoft 365' on a screen associated with Office 2013, and vice versa.
Keep in mind that both Office 2013 and Office 365 are new kinds of products, so over time we will all be that much more comfortable with these new ways of approaching productivity. Questions? Just let me know!