Earlier I studied macroeconomics from Blanchard. But now while reading Mankiw's Macroeconomics I found different definition for natural rate of unemployment. According to Blanchard,
"the rate of unemployment (and by implication the level of output) that prevails if the price level and the expected price level are equal." (pg. 135, sixth edition) and
"The natural rate of unemployment is the rate of unemployment required to keep the inflation rate constant." (pg. 170, sixth edition)
But according to Mankiw,
"The natural rate is the rate of unemployment toward which the economy gravitates in the long run, given all the labor-market imperfections that impede workers from instantly finding jobs."(pg. 177. eighth edition),i.e., where unemployment rate reaches steady-state, it neither increases or decreases, where rate of job finding is equal to rate of job separation.
What is the common ground between all these definitions? Are they different or essentially the same? If so, then how?