They should be synchronized.
This is important for Python applications and other applications that may be "indentation-sensitive".
If the tabulator size is set to 4 (under Preferences>>Editor) then pressing the tab key will in fact move the cursor over 4 places to the right, however the column numbering (as displayed in the footer of the editor window) only increments by a factor of 1 (when it should be 4). Python outputs a crash error if, for example, a person produces code where on one line he hits the spacebar four times to produce an indentation, and for other lines he uses the tab key, because although it looks visually aligned, python interprets this as different indentations (when there really is none visually, and when the programmer does not intend that there be indentation differences!). This seems like it should be an easy fix - - - please fix this, thanks!