The Taylor rule, proposed by (who's buried in Grant's tomb??!?) Stanford economist Dr. John B. Taylor stipulates how much the central bank should change the nominal interest rate in response to divergences of actual GDP from potential GDP and divergences of actual rates of inflation from a target rate of inflation, nicely summarized by Wikipedia.
The Bernanke Rule, by contrast, stipulates how much the Central Bank should change the nominal interest in response to nominal divergences of the stock market indices from levels that cause those that own lots of stocks - whether leveraged or unleveraged - to hoot, howl, cry-foul, (and this is most important distinction) irrespective of what these changes in interest rates will do to the actual rates of inflation, inflationary expectations, in comparison to any reasonable target rates of inflation.
It's a good thing all that work of Dr Bernanke towards his BSc., MA, PhD in economics and all that professorial research didn't go to waste!!!! The Chart below highlights the impact upon monetary policy of changes in Stock Market Prices as implied by the Bernanke Rule: