Office 365 and windows Azure are Cloud based terminologies.
In the Cloud-
Microsoft is trying to keep all their products.
Ex: Windows, Office,exchange...
So what they did, then grouped some products and names it.
In Office 365, they are keeping all Office related products. Like: Office suite (Word, excel, PPT, one note,.....), SharePoint, Exchange, Lync.....
In Windows Azure, then will keep all OS related products..
in SQL Azure, then will keep SQL related software.
So if some one talk about SPO or SharePoint online, or Cloud or Office 365. All are related to above diagram.