Basically we have applications running on platforms consisting of an operation system like Windows and a runtime environment like .NET. The application itself is developed with an IDE like Visual Studio. The system with the application is part of an environment consisting of
Mechanisms for persisting data (SQL Server, SharePoint lists)
Communication and processes (BizTalk Server)
Identity management (Active Directory).
Most companies today use on-premise software which means the software is running on an infrastructure inside their own companies buildings.
Another kind of application platform is the Cloud Platform where Cloud Services are running which can be divided into the following categories:
Software as a Service (SaaS): The application runs in the cloud and can be operated by the browser. (like an online CRM system)
Attached Services: The application runs in house and uses additional services from the cloud. (like Windows Update)
Cloud Services: On-premise software or applications from the cloud are enhanced with additional functionalities.
The combination of on-premise Software and Cloud Services is called Software + Services (S+S) which just means software running on an infrastructure in house plus additional functionalities from the cloud.
The Azure Services Platform is a combination of different technologies in the cloud:
Windows Azure: A Windows based runtime for applications with the possibility to store data.
.NET Services: The services offer interfaces for access control, communication and workflows.
SQL Services: The services offer an interface for storing data.
Live Services: The services offer a framework where you can access the Microsoft Live applications and their data.
SharePoint Services & Dynamics CRM Services: These services offer functionality for collaboration.
All technologies from the Azure Services Platform can be used independently or together.
If we summarize the things above we have the following SharePoint platforms:
Windows SharePoint Services 3.0 (and earlier versions)
Microsoft Office SharePoint Server 2007 (and earlier versions)
Microsoft SharePoint Online
Microsoft SharePoint Services