Both of them may be caused by a cold, and cough is usually caused by the late stage of a cold, which is also difficult to get better. Moreover, it is also quite harmful. If it is not treated, it may hurt the heart and lungs.
A runny nose may also be caused by a cold, but it is usually the first symptom, or it may be rhinitis, and then a little cold will make your nose unbearable. Children with runny noses are common.