*Update: With the release of Office 2016 (22nd September 2015) you may wonder how and when you can update the version of Office you use with your Office 365 for business subscription. Check following links to find out what version of Office you are running and how to update to the latest version of Office.
What version of Office am I using?
How do I update Office to Office 2016 using Office 365 for business?
Download and install Office using Office 365 for business on your PC

'In Office 2016, you can control how fast your users receive feature updates to Office 365 ProPlus. One choice is a monthly update to Office 365 ProPlus, which can contain new or updated features, bug fixes, and security patches. This is called the Current Branch release.
If you prefer, you have the option to receive only security updates for Office 365 ProPlus each month, and instead defer for several months receiving any features changes and bug fixes. A few times a year, we’ll provide an update to Office 365 ProPlus for you to test and deploy that contains those feature changes and bug fixes. This is called the Current Branch for Business release.'
From: Prepare to update Office 365 ProPlus to the Office 2016 version

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Microsoft Office suites have traditionally included desktop version of applications such as Word, Excel, PowerPoint, and Outlook. All the new Office suites (for example, Office Professional 2013) include the latest versions of these applications. These suites do not come with any cloud-based services included in Office 365 plans.
Office 365 refers to subscription plans that include access to Office applications plus other productivity services that are enabled over the Internet (cloud services), such as Lync web conferencing and Exchange Online hosted email for business, and additional online storage with OneDrive and Skype world minutes for home.

Many Office 365 plans also include the desktop version of the latest Office applications, which users can install across multiple computers and devices. Current Office application versions for Office 365 are based on Office 2013 for Windows and Office 2011 for Mac. Customers with an active subscription will be entitled to the newest versions when available!

Office 365 ProPlus is the version of Office that comes with many Office 365 plans but it is also available as a standalone offering, as shown below.

In the following table you can find availability of Office applications, and possibilities for Office Add-ins support, across Office 365 business plans (*) and volume licensed editions of Microsoft Office 2013.

Feature	Office Professional Plus 2013	Office 365 ProPlus	Office for Mac 2011 in Office 365	Office 365 Business Essentials	Office 365 Business	Office 365 Business Premium	Office 365 Enterprise E1 Office 365 Education A2 Office 365 Government G1	Office 365 Enterprise E3 Office 365 Education A3 Office 365 Government G3	Office 365 Enterprise E4 Office 365 Education A4 Office 365 Government G4	Office 365 Enterprise K1 Office 365 Government K1
Office Applications	Yes	Yes	Yes	No	Yes	Yes	No	Yes	Yes	No
Office Add-ins, ActiveX support **	Yes	Yes	No	No	Yes	Yes	No	Yes	Yes	No

* If you are unsure about your Office 365 subscription, please see this Microsoft Office 365 comparison chart, Compare all Office 365 for business plans

**Not applicable for Office on Demand - It is not possible to customize Office on Demand applications with add-ins, dependent applications, or other customizations unless they already exist in Office installations. The Office on Demand application does not register itself in the system or automatically associate with Windows file types.

Update: Office on Demand feature will be removed from Office 365 ProPlus starting November 2014.

What is Office 365 ProPlus?

Office 365 ProPlus is the version of Office that comes with many Office 365 plans. It includes Access, Excel, InfoPath, Lync, OneNote, Outlook, PowerPoint, Publisher, and Word.
Project, Visio, and SharePoint Designer aren't included with Office 365 ProPlus, but are available in some Office 365 plans.

Office 365 ProPlus is just like Office 2013 in many ways:
-When you deploy Office 365 ProPlus, it's installed on the user's local computer.
-Office 365 ProPlus is a full version of Office. The programs have the same features and functionality as other versions of Office. For example, Word in Office 365 ProPlus works the same way it does in Office Standard 2013.
-Its system requirements are the same as for Office 2013.
-Like other versions of Office, Office 365 ProPlus is available in a 32-bit and a 64-bit version. (32-bit version recommended to deploy, even on computers using 64-bit operating systems)
-Office 365 ProPlus is not a web-based version of Office! It runs locally on the user's computer. Users don't need to be connected to the Internet all the time to use it.

What is the difference between Office 365 ProPlus and Office Professional Plus 2013?

Both Office Professional Plus 2013 and Office 365 ProPlus deliver the same application experiences. However, Office Professional Plus 2013 is a traditional Office installation that is tied to the computers it is installed on, and it is available through volume licensing only. A user-based service, Office 365 ProPlus is available as a subscription.
Office Professional Plus 2013 uses Windows Installer Package (MSI)-based installation. Office 365 ProPlus uses Click-to-Run installation and software update management.

Last a note about difference in the location of Office 2013 and Office 365 ProPlus installation on your computer. For example used here comparison is done on Windows 8.1 computer with Office 32-bit version.
Outlook 2013 installed from Office 365 E3 subscription with Office 365 ProPlus license is running from: "C:\Program Files\Microsoft Office 15\root\office15\OUTLOOK.EXE".
Outlook 2013 installed from Office 2013 Volume license is running from: "C:\Program Files (x86)\Microsoft Office\Office15\OUTLOOK.EXE".

Office Deployment

There are two different ways that you can deploy Office, either the Windows Installer-based (MSI) version or the Click-to-Run version, to users in an organization.
Windows Installer (MSI) is the traditional Setup architecture for installing Office products and languages. It is the same setup architecture that is used in Office 2010 and Office 2007. Office Standard 2013 is an example of a Windows Installer-based version of Office.
Click-to-Run is a newer setup architecture and is based on Microsoft streaming and virtualization technology. This technology reduces the time that is required to download, install, and update Office products and languages.
Office 365 ProPlus is an example of a Click-to-Run version of Office.

Click-to-Run
Click-to-Run uses virtualization technology to run Office applications in a self-contained environment on a local computer, which allows users to run Office applications side-by-side with earlier versions of Office.
Office 2013 Click-to-Run is a technology that reduces the time that is required to download and use Office 2013 client products. The streaming technology lets you use a Click-to-Run program before the complete program is fully downloaded and installed on your computer.
Retail and Small Business copies of Office are only available as "Click-to-run". While this should work the same as the traditional installed (aka MSI) version, a few add-ins that haven't been properly updated for Office 2013 may not work.
If you have an Office 365 E account that includes Office you can try to convert to an MSI install using instructions from: http://www.slipstick.com/office-365/convert-office-2013-click-run-msi-installation

Even though the Office product runs in a self-contained environment, the Office product can interact with the other applications that are installed on the computer. Macros, in-document automation, and cross-Office product interoperability will work. Click-to-Run is also designed to allow locally-installed add-ins and dependent applications to work with it. However, there is the possibility that some add-ins or other integration points with Office might behave differently or might not work when you are using Click-to-Run.
Note: Office 2013 Click-to-Run changed the run-time so it supports add-in better than Office 2010 Click-to-run. Office 2013, the VSTO Runtime is designed and tested to work both against MSI and Click-to-run installations.

Office 365 ProPlus running in an RDS (Remote Desktop Services) or TS (Terminal Services) environment
Currently, Office 365 ProPlus will not physically install in an RDS/TS environment.  There is an exception in the Product Use Rights that allows customers to install a VL/MSI copy of Office Professional Plus 2013 on the RDS/TS server and then users can utilize one of their 5 activations of Office 365 ProPlus to access it.
"Unlike managed volume-licensed environments, currently, Office Professional Plus for Office 365 cannot use Microsoft Application Virtualization (App-V) or Windows Server 2008 Terminal Services as deployment options. Because Office Professional Plus for Office 365, included in MSDN  is based on the Retail SKU, it cannot be installed on a Terminal Server.
The customer will have to download the VL version from VLSC to install on Terminal Server."
Native RDS/TS support for Office 365 ProPlus is coming, and is currently targeted to release in the second half of 2014.  It will support Office 365 ProPlus installations on Windows Server 2008 R2 or newer with RDS enabled.

How to: Install Office 365 ProPlus

Office 365 ProPlus installs as one package. That is, users can't install Word and PowerPoint, but not Access. If you don't want users to run a particular program, such as Access, you can use AppLocker. Or, you can deploy Office 365 ProPlus to your users by using Microsoft Application Virtualization (App-V) 5.0. App-V 5.0 lets you choose which programs to install.
One of the ways to deploy Office 365 ProPlus is to have your users sign in to the Office 365 portal, go to the software page, and then select Install.  This self-service method is designed to provide flexibility, unlock consumerization of IT scenarios (such as installing Office 365 ProPlus at home), and is a key enabler of the ability to install Office 365 ProPlus on up to 5 devices. However, keep in mind that users must be local admins on their computers to install Office.

To install Office from Office 365 portal:
-Log in to Office365 portal.
-Click "Office365 settings" (in the top panel next to your account name)
-Click "Software"
-Select "Office" from the left navigation menu. From here you can install the latest version of Office.
-Select your language
-By default, the 32-bit version of Office will be installed. If you prefer to have the 64-bit version, click the advanced link  (as shown in the picture below)
-Click the install button
-and Wait...



Finally the 'You're good to go' screen will open. Click the 'All done!' button. The installation process is now complete and you can start using Office 365 ProPlus - Office 2013 applications.

Not sure if you are running Office 365 ProPlus or Office 2013 Professional Plus?

The easiest way to find out is to check in Control Panel under Programs and Features.

If you have Office 365 ProPlus installation you will see following listed among Programs


or


For the Office 2013 Professional you will see following



Note that Office 365 ProPlus is shown in About box of Office applications as Office 2013 (see below) and in registry it under the Office15, just like Office 2013.