From the API document for OpenLayers, I can tell that a
FramedCloud has more functionalities than
Framed, which in turn has more functionalities than
Anchored. I am hoping for someone to describe these differences in a way which a lay person like me can understand.
As @randlet and @Aragon mentioned, You might want to have a look at the following example: Popup Matrix
That only compares Anchored and FramedCloud variants. Visually one can see that the FramedCloud class Popup looks like a speech bubble with a arrow pointing to the anchor. Anchored class Popup is just a rectangle.