Let me clarify a bit.
The webpart in CMSSiteManager>Development>Webparts is the base object you are using instances of on page templates. This is where you set the definition of the webpart (name, location in file system, description, properties, etc.). This is versioned as an object.
The webpart you place on a page template in the CMSDesk is an instance (or snapshot at that time) of the definition of the webpart you have defined in the CMSSiteManager. This is
the definition of a page template and gives how you an idea of how it all works together.
If you make a change to the webpart properties on a page, you will see in content staging in the CMSDesk that you will have a task that states Update page template "template name". When you go to CMSSiteManager>Development>Page templates, you will see in the versions tab that there is also a new version.
If you make a change to the content say in the editable text webpart, that is stored in the document itself and IS versioned in the (PageName)>Properties>Versions under the column DocumentContent.
I'm not sure what webparts you are using to display your content but a webparts
properties are all saved to a page template and NOT a document. There are only a few unique webparts that store their
content to a document for instance the Editable Text and Editable Image webparts. Whatever is entered/saved in the documents "Edit" tab will be saved with the document. Whatever is entered/saved in the documents "Design" tab is saved with the page template.
Hope I didn't confuse you more.