SharePoint is the cloud sibling of the SharePoint family. It comes with your Office 365 Subscription. Microsoft Initially built SharePoint solely for on-premises but since the launch of SharePoint Server 2013, they have also come out with their cloud product.
The advantages of SharePoint Online is the end users get acquainted with the latest features from Microsoft. It is easier for Microsoft to release new features to the cloud rather than the On-Premise version. Hence, the cloud version gets newer features and updates before the On-Premises Version.
With SharePoint Online and Office 365, Microsoft has created a new view or look for SharePoint itself. It translates to the entire SharePoint Online Infrastructure. There have been changes to the appearance of Items in the Menus and some of the menus which were quite prominent in the On-Premises version is not there. They have tried to make use of the Office 365 ribbon and have tried to transfer most of the functionality over there.
If a user is not comfortable with the the new look, he can switch over to the old view at any point of time. There is a link at the bottom left hand corner which says “Switch to Classic view”. There is a perceptible difference in the appearance of the old and new view, just to give you an Idea here is the view of a Document Library. This is a view from the New look
And this is the old view
See the difference? The old view has a menu for the library which Includes difference functionality which is not there in the new view. So if you happen to be in the old view and want to come back to the new view, simply close your browser and open it again, this would delete the cookies associated with the old view.