The NAIRU, the rate of full employment, and the natural rate of unemployment are often conflated. But they are not the same.
The natural rate of unemployment, as that term is defined by the Congressional Budget Office, “is the rate of unemployment arising from all sources except fluctuations in aggregate demand”. As the close-to-full-employment rate in 2000 was at least partly caused by a fluctuation in aggregate demand, the natural rate of unemployment was, in fact, higher.
The NAIRU (non-accelerating inflation rate of unemployment) is the lowest possible rate of unemployment that can exist in a free-market environment without the acceleration of the growth rate of nominal wages, and, therefore, nominal prices. From historical experience (mostly from before 1970), the U.S. NAIRU used to be ~4.3%. From post-1985 experience, it also looked to be ~4.3% at the turn of the millennium. During its peak in the 1970s, it was ~7.8%. But this was mostly due to a combination of structural changes in the economy, and, to a lesser extent, to the entry of millions of Boomers and females into the labor force. These structural changes are long past, as is the Baby Boom and the entry of females into the labor force. So the NAIRU most likely remains ~4.3%, if not lower.
The rate of full employment is the rate of unemployment when the number of job openings becomes equivalent to the number of unemployed. This has probably never happened in the United States since at least 1970, but the closest the U.S. has gotten there since my birth has been in April 2000, when the unemployment rate was 3.8%. In December 2000, when the unemployment rate was 3.9%, the number of unemployed in the United States was still higher than the number of job openings. Consequently, the rate of full employment in 2000 must have been somewhere below that; most likely between 3.5 and 3.7%. From the looks of things, the number of job openings and the number of unemployed in the United States in the recovery from the Great Recession is most likely to equalize at around 6.5 million workers, or at an unemployment rate of 4.0%. Imagining current economic trends continue, the U.S. will reach full employment and the NAIRU in about two years, if that long.