the White VS2 are also not interchangeable with Singer. In fact, Singer was a rather unique looking shuttle, and shorter than most. Singer shuttles have an indentation in the middle (a waistline) so they are very easy to identify.
The White shuttle is unique in that it has a pin in the center and the bobbins are hollow. I've not gotten around to start experimenting to see if other shuttles would actually work - though the bobbin winder is designed to work with a hollow bobbin. In the early 1900's Boye examined the different shuttles companies used, and came up with 12 to cover the most common machines. I sort of take this as a good indication that a shuttle for one machine won't work in another or Boye would not have made different ones.
The Free VS machine does take the same shuttle as the Singer - however Singer made a change to it's shuttle carrier that resulted in a slight change to the shuttle - it's either downward compatible or upward (but not both) I don't' remember which way though.