The simple answer is that the numbers come from two separate surveys that survey two different entities. The number of unemployed (and the unemployment rate) is estimated using the Current Population Survey. This is a survey of households. It, basically, asks individuals what they're doing with their time.
The second is the Current Establishment Survey. As you may guess, it surveys establishments (businesses, non profits, schools, government agencies, etc.). This survey asks establishments to report the number of employees, hours worked, etc. It is important to note that the Current Establishment Survey ONLY captures *payroll* jobs. If you are a lawyer, consultant, sole proprietor, etc, you are not on a payroll job, so you can be employed but not show up in the payroll jobs numbers. Or vice versa. The reason the payroll jobs figure is often adjusted is because smaller establishments tend to be slower at returning responses. You can gauge how small businesses are doing compared to larger establishments by looking at the adjustments.
Also, neither survey counts the institutionalized population which includes the military. So if there is a military drawdown, those don't count as payroll jobs lost but will show up as people entering the civilian workforce. Same with people going in and out of jail.
So these are separate *indicators* of how the labor market is faring. They are not directly compatible measures. They work very well as indicators and estimates but are not direct measures. We expect them to move together over time--which they do--but on any given month there may be some statistical noise.
The best measure we have of unemployment is the CPS. The best measure we have of payroll jobs is the Quarterly Census of Employment and Wages. The QCEW is based on information provided to state UI programs but isn't available for up to a year. Historical payroll job data is updated every Feb for the year prior. A few weeks ago the data for 2011 was updated, and 2011 was a much better year for payroll job creation than the CES indicated.
I hope this answers your questions. That will be $150 unless you would like to put me on retainer.