Simplisticly: A heading hold gyro... tries to maintain a compass course. A rate gyro tries to limit the rate of change of rotation.

So...

Yes, the heading hold will result in the tail of the heli or airplane "locking" on a chosen direction. (not very good for a plane at all... I can't think of a good use for it) and n forward flight of the heli... its best to turn heading hold function off. (they have that option...)

If you are GOOD at flying a heli... let the rate gyro have full tailroto cntrol for a while. Watch the rate of yaw slowly increase in hover. (that will prove your tailrottor is trimmed for a different main rotor load than your steady state hover)