I just assumed, it being called Running, that it only applied to your running speed. But I’ve made a few assumptions about ACKS that are totally wrong, I am interested to hear the answer too.
Base movement speed is 120' per turn when exploring, or 120' per round running. Running proficiency increases your speed to 150' per turn when exploring or 150' per round running. Combat move is 1/3 running speed, so it would be 50' per round.