Not exactly. A stage check is a scheduled test of your flying knowledge and abilities performed by a Stage Check Airman (An experienced CFI that is employed with the school). At our school stage checks are scheduled intermittently throughout the course of the professional pilot program. Everything from our pre-private training through our CFII is broken down in to various stages with numbered lessons within those stages.

For us stages one through three are pre-private stages. At the end of stage one we take a stage check and upon passing that stage check we begin stage two which begins with our first solo. Stage two is our cross country and night preparation and upon the completion of the stage two check we begin stage three with our first solo cross country and solo night flights and night cross countries. At the end of stage three and upon completion of the stage three check we are approved and deemed ready to take the FAA private pilot checkride with a DPE (Not affiliated with the school mind you). This process continues through the Instrument rating, CMEL, CSEL addon, and the CFI and CFII stages.

Basically a stage check is a failsafe to make sure that you are being taught correctly, that your are progressing in your training and that you are ready for the next step in the training process. They really don't have anything to do with the FAA with the exception of the fact that we are not authorized to take check rides without completing a stage check and being approved.