Would you expect the natural rate of

unemployment to be roughly the same in different countries?

The level of unemployment that exists even when the economy is stable is referred to as natural rate of unemployment. This unemployment results from the combination of economic, social, and political factors that occur when economy is stable and growing strongly. Natural rate of unemployment is determined in long run by economic supplies and production possibilities.

natural rate of unemployment varies from county to country because each countries' public policy differs from each other.

Suppose there is a country A where a worker looses its guaranteed job medical benefits and welfare, food. there will be a low opportunity cost to remain unemployed and he will be less willing to work.

on other hand country B where government offers all support for job research or training this workers to work.

In country A NRU is high because of their policies. It demotivates worker

In country B there is low NRU and these policies make people motivated towards work.