Can horses learn two different types of reign control, such as neck reigning and others?

Potentially yes. What Cara mentioned is correct and neck reigning is aWestern thing, but a horse can learn two different ways to respond to the reign just as they can learn two different disciplines.
Neck reining for western. Girl English rider we use the bit . We pull the left rein
To go left and right to go right. Not literally pulling but yh
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