What is the main difference between Class C and B Radar Service? What is the main difference between Class C and B Radar Service?


  Class C service provides approved separation between IFR and VFR
  aircraft, and sequencing of VFR aircraft to the primary airport. 
  
  Class B service provides approved separation of aircraft based on IFR, VFR,
  and/or weight, and sequencing of VFR arrivals to the primary
  airport(s).


What does approved mean?
The term is not "approved", it is the complete phrase Approved Separation. This is the standard FAA term for what was previously called either standard separation or radar separation, and means "separation in accordance with the applicable minima in [FAA Order 7110]".

The separation minima are further defined in the JO 7110 family of FAA Air Traffic Control orders, which you can find linked from the page above.