Personally, I'm against flaming "on the web", but this is just another stupid MS marketing move, another in a long history of stupid marketing moves and frankly I'm incensed!  Specifically "reusing" the same name for different products:
- OneNote (for Windows vs for Office is the most recent example before this one. "For Windows" is another "improvement" that is missing key features!)
- OneDrive (for Business vs for Consumer)
- Skype (for Business vs for Consumer)
- Office 365 (for Business vs for Consumer: look at the license terms)
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Right, you've simplified 2 words, "Office Online" into 4, "Office for the Web".
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Thanks for nothing!  This (dis)"improvement" just adds to the confusion.
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Since it Office Online apps are the most dumbed down version of "Office", it is vital for users asking for help to qualify exactly which version they are using. It is bad enough when people already use the "Office" umbrella to ask questions about Office for Mac in an Office for Windows forum. Office Mac STILL has fewer features than Office Windows. So if the user follows your advice and simple calls it "office" or "Word", they get the wrong answer! The specific example I encountered yesterday is "Photo Albums" in PowerPoint.  According to MS documentation, the mac version still does not support that feature:
https://support.office.com/en-us/article/photo-albums-aren-t-available-in-powerpoint-for-mac-1db1a051-c3bc-4e42-9e93-304f62fa9a9c
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