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