Ok, here's the explanation, as it was explained to me by Kishore, of how all this works together. I think if Dassault would have explained this years ago, at least the concept of the 3DExperience platform, there would be much less confusion and backlash.
So, mySolidWorks is the web-based hub for all SolidWorks products, both desktop (SolidWorks, MDB, SWCD, SWID, Visualize, Composer, etc.) and cloud (Xdesign, Xdrive, etc). All of this together makes up the 'SolidWorks Innovation Platform'. Dassault's 3DExperience platform is the underlying layer that provides the tech/services for all of those products (just as parasolid kernel, owned/developed by Siemens, is used by those products).