Based on my understanding, putting a table for everyone’s reference. I will not delve into pre-2001 history.
|Version||Assembly Version||Licensed Product – Better/Higher Product||Base Platform, Product with Limited Features, Free Version|
|2001||x||SharePoint Portal Server (SPS) 2001||SharePoint Team Services (STS)|
|2003||v11||SharePoint Portal Sever (SPS) 2003, Microsoft Content Management Server (M CMS) 2002||Windows SharePoint Services(WSS) 2.0|
|2007||v12||Microsoft Office SharePoint Server (MOSS) 2007||Windows SharePoint Services(WSS) 3.0|
|2010||v14||SharePoint Server 2010||SharePoint Foundation 2010|
|2013||v15||SharePoint Server 2013||SharePoint Foundation 2013|
* v13 skipped due to 13 being considered unlucky number by many customers.
Portal from SPS 2003 was dropped as it lead people to believe that it can be used
only for Portal development and nothing else.
Office from MOSS 2007 was dropped as it lead some people to believe that it is an Office product like Word and Excel.
Hope Microsoft has got the name right this time with SharePoint Server 2010.
Update: No change in name with the release of SharePoint Server 2013
Cloud: SharePoint can be deployed On Premise or On Cloud.
The Microsoft Cloud versions of SharePoint are called BPOS Standard, BPOS Dedicated, Office 365 / SharePoint Online.