The answer to this question depends on what you are looking to get out of Office 365. The name of this Microsoft solution is a bit misleading, but I think this latest iteration, an expansion beyond the long-lived desktop software, it is much more appropriate. An office is much more than just a document, or spreadsheet after all.
But can Office 365 and SharePoint be used interchangeably?
The short answer is no, for a couple of reasons. First, the home edition of Office 365, Office 365 Home Premium, is simply the Office desktop applications, plus OneDrive (SkyDrive), and Skype. While the Office desktop applications are built with tight integration into SharePoint, and can leverage SharePoint capabilities, the applications themselves are not SharePoint. Skype and OneDrive are also standalone applications that are not part of SharePoint. OneDrive for Business (formerly SkyDrive Pro), however, is SharePoint, but it is not offered in the home edition. I will talk about that a little later.
SharePoint enters Office 365 at the business edition level. All versions of Office 365 for Business, save one (Exchange Online Plan 1), utilize SharePoint in some way. I'll start at the Small Business level.
Office 365 Small Business
Office 365 Small Business and Small Business Premium begin to utilize SharePoint (Online) in the slightest way. Both plans offer OneDrive for Business, which under the covers, is actually a SharePoint document library (or app if you're into the hip new naming convention of SharePoint 2013). The OneDrive for Business document library resides in the user's SharePoint Online Mysite. The OneDrive for Business desktop application is essentially a derivative of SharePoint Workspace, which allows users to synchronize SharePoint lists and libraries on her/his desktop. By default the OneDrive for Business desktop app syncs with the users OneDrive for Business library, but users can also synch other libraries using the same tool. Bear in mind that there is no OneDrive for Business application for Mac at the time of this writing, and the Android and iOS OneDrive for Business apps do not synch to libraries beyond the default OneDrive for Business library.
As I mentioned before, the "real" SharePoint begins in Office 365 Midsize Business. More control over the SharePoint environment becomes available, as do more features through the SharePoint Online Admin page. More site collections and sites can be built, plus more site customization can occur at the Midsize Business level. Features like the Content Organizer and Records Center sites are enabled, but other SharePoint Enterprise level features like Business Connectivity Services (BCS), eDiscovery, and Business Intelligence, are not. You need to be at the Office 365 Enterprise E3 level to get those.
If you are looking for the full blown SharePoint Online, you need to sign up for Office 365 Enterprise E3 and above. While this is still not exactly the same as SharePoint 2013 Enterprise on-premise, it is as much SharePoint as you can get in Office 365. It now enables features like eDiscovery, the BCS, and Business Intelligence (but not PerformancePoint services for some reason). Plus, it adds some Office SharePoint services like Excel Service and PowerPivot.
So, back to this Office 365 SharePoint...
As I said earlier, it really does depend on what you want to get out of it. If you wish to simply use Office applications (Word, PowerPoint, Excel, etc.), then you choose to continue to simply use the applications provided by Office 365. If you are using an Office 365 business level subscription, you can add email into the mix, and a little enhanced collaboration.
However, if you want to leverage Office 365 to automate document processes, enforce document or records policies, or at the very least, have an efficient file management capability that goes far beyond your typical fileshare*, then you are using SharePoint. This really shifts the tables from the application perspective of Office 365 to a document management perspective. You cannot get this from the applications alone, and therefore must leverage SharePoint to make this work. If you view Office 365 from this perspective, then you are beginning to view it more as SharePoint and not simply Office.
From this view, one can see that Office 365 is evolving to be more inline with what goes on in an office. It is a series of solutions for doing, and no longer just for working. It all depends on how you look at it.
* The capability to do powerful file maintenance and document management is available to you, but you have to configure and enable it. This is not an easy task. My SharePoint Business Professional™ program offers instruction on how to get the most out of your SharePoint environment from a business perspective. Check it out.