What is Microsoft Office SharePoint Online?
First of all, you need to understand what Business Productivity Online Standard Suite is.
Microsoft Business Productivity Online Standard Suite is a set of messaging and collaboration solutions hosted by Microsoft and consists of Exchange Online, SharePoint Online, Office Live Meeting and Office Communications Online (coming soon).
https://www.microsoft.com/online/en-au/business-productivity.mspx
Ok, then what about Microsoft SharePoint Online?
Service Description for Office SharePoint Online Standard
Microsoft® Office SharePoint® Online is a collection of Web-based tools and technologies built on Microsoft Office SharePoint Server 2007 that help you store, share, and manage digital information within your company.This white paper describes the services and features that are included with the Standard offering of SharePoint Online.
https://www.microsoft.com/online/en-au/sharepoint-online.mspx
What can I developed in MOSS online standard offering?
Microsoft SharePoint Online Standard Developer Guide