Service ceiling is the height at which the aircraft can maintain 100 ft/min climb rate, using continuous power, and is always specified at best climb speed. As FixedRotaryWing says, this means the rotor is at its most effecient point, so the service ceiling can be very high.
The HOGE ceiling is the max hover height at takeoff power, always lower than the service ceiling because the hover power required is quite high, so the engine must be at a much lower altitude in order to produce it.