Okay, I think it represents the generalized type of data source.
From what I'm seeing in my Data Sources:
1 = A real database
2 = A published data source (data exists in the Tableau Server). It is clickable and will take you to the data source's information page.
3 = A file such as text, Excel, etc.
An icon without text following it indicates the data came from the Clipboard:
Just hope you don't get this, a published data source icon that is NOT a published data source but really an embedded one...that has no connection info when you click it :
See, it's an embedded data source and does not show up as a published data source anywhere:
The workbook that uses the data source refreshes fine, no Server Alerts!
Kinda-sortaish but not.
I believe the icon in the Connects To column is just an embellishment from the Connection Type column.
I thought it was pretty self-explanatory in the image above. You just may wanna make sure you have the necessary permissions