One of the main differences between spotting a front hip circle down and a whole front hip circle to support is that for the complete skill the spotter places himself on the same side of the bar that the gymnast starts the skill.
Notice how after the back pull over the coach switched sides to spot the front hip circle to support when the gymnast begins to speed around. The coach standing on the left side spots the hamstring area with his left hand and his right hand spots the gymnast’s back. If he is just spotting a front hip down he switches to the other bar side again.
In the front hip circle to support one of the functions of the hand spotting the hamstring area is keeping the pressure of the legs against the bar; a technical requirement to complete the whole skill. If the legs fall away from the bar while circling, the skill can not be completed correctly. The hand spotting on the back also helps to keep the body pressure on the bar and assist bringing the gymnast back to the support if she runs out of circle momentum.
To create front hip circle speed, it helps to begin with the legs making bar contact around the mid thigh. In this example, the gymnast may push up some more because the bar is too close to the hips so her center of mass is low and she will come down slower.
Another important component of a succesful front hip circle to support is using the arms to pull the legs against the bar. When the gymnast with her center of mass raised leans forward from the support position it creates a slight imbalance that makes the body fall down by gravity.