Federal Reserve Bank of St. Louis has a good explainer on the different unemployment rates. (Click the header for the link).
These nuances have become more important than before as Donald Trump has frequently suggested that the unemployment rate is fake. While Trump overstates his case, it’s also true that the headline unemployment rate is misleading.
In addition, during and after the crisis, the civilian participation rate dropped. 
In the above chart, which is the inverse of the labour participation rate, the fraction of the population not in the workforce is shown. As the blog explains, it comprises of:
Principally, these are retirees, students, people with various handicaps, people who dropped out of the labor force, and people who do not want to work
Of course, there’s a thin line between people who are discouraged to work and people included above. As you can see from the chart above, the fall in the participation rate has been coincident with the crisis and raises the question if the unemployment rates sufficiently capture true unemployment. It is difficult to believe that this is entirely due to demographics.
So it’s important to keep these things in mind when discussing politics. Neither believe a nationalist, nor a neoliberal.