Stickies can be moved grasping them anywhere in the "move" area (that is the area of the sticky not dedicated to the text input or to the resizing).

The mouse cursor ove the "move" area is the classic "arrow" cursor, while on the text area cursor is the classic 'IBeam' related to text areas:

In the above figure the area right to move the sticky is in yellow color ("arrow" cursor). In light blue the text area, in pink the resizing area.