Video: Office 365 vs OneDrive

Microsoft Office 365 is commercial software plus services offering a set of products from Microsoft. Office 365 includes the Microsoft Office suite of desktop applications and hosted versions of Microsoft's Server products (including Exchange Server, SharePoint Server, and Lync Server), delivered and accessed over the Internet, in effect, the next version of Business Productivity Online Suite (BPOS). Office 365 free alternatives are Zoho, Google Apps.
Tools for online file/docs storage and collaboration. Contains Web versions of Microsoft office editors (Word, Excel, PowerPoint, OneNote). Excel web version allows simultaneous document editing in real time. OneDrive alternatives for enterprise are: Box, Office 365, Sharepoint.
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2014 - Microsoft makes Office free for iPhone, iPad and Android to win over OneDrive

Microsoft made its full-fledged Office apps free on iOS and Android. The update adds standalone Word, Excel, and Powerpoint apps for iPhone. Previously, there was a single Microsoft Office app that allowed users to view Word, Excel and Powerpoint files and make basic edits, but the individual apps didn't have their own offerings for iPhone. The new iPhone apps have the same advanced editing capabilities as their iPad counterparts, though they've been optimized for the smaller-screened iPhones. Microsoft is also finally launching Office apps for Android tablet, which are still in the works and expected to become available in 2015. The update greatly expands the apps' capabilities for free users, who can now create and edit documents in Word, Excel and Powerpoint without an Office 365 subscription. Previously, users couldn't create or edit files without forking over $99 per year.

2012 - Microsoft Office gets own (cloud) App Store - a new advantage over OneDrive

Nowadays any popular service or application should have its own App Store, because the third-party developers want to build add-ons for popular products, and users - are eager to buy them. So Microsoft Office also gets the own app store - Office Store. Of course, it will only work with Office 2013, so that users had another reason to upgrade. For example, it contains an app that displays maps with points in Excel or an app that shows the LinkedIn-profile for a contact in Outlook. Interestingly, the Office Store will include only cloud applications. There will be no Visual Basic macroses. The advantage of this approach is that you don't  need to install additional apps. Microsoft does not restrict developers in selecting the cloud platform on which the application is hosted. It can be Azure or Amazon or other platform. The revenue split is more favorable than other app models, with an 80/20 split (the devs take 80%).

2011 - Windows SkyDrive moves from Silverlight to HTML5 to keep up with Office 365

Microsoft has finally killed the intrigue on the future of Silverlight in web-applications (recall this intrigue emerged at the end of last year). The new version of the online file storage Windows SkyDrive (which works as the basis of all Windows Live services) is completely rebuilt on HTML5 instead of Silverlight (even video player is now working on HTML5). SkyDrive is now much faster and supports all browsers (even Google Chrome). Along with the underlying technology shift, the developers have rebuild the service interface - it's now very similar to the Windows folder interface. Moreover, users of Windows 7 and Internet Explorer 9 can get to SkyDrive directly from the taskbar and with one click create Word, Excel, PowerPoint documents in Office Web Apps online editors:

And when working in the online SkyDrive folders user can open documents in the online editors as well as in desktop Office 2010. In the second case, the document is automatically saved back to the online folder.

Recall also that, unlike the new Apple iCloud, Windows SkyDrive allows to create collaborative workspaces and share documents with your team (and the developers promise to add the editing permissions to these shared folders).