A "mutation" is a permanent alteration of the genetic composition of an individual. To obey this definition, a base change in one strand must be accompanied by a corresponding change in the opposite strand. Only in this way a mutation can be transmitted to the offspring.
The situation where only one of the strands has undergone a base change constitutes a pre-mutational DNA damage, as the double strand will show a deformation at that site. The enzymes of DNA repair mechanisms recognize and correct many such "deformations", but sometimes they do not know which was the original base, and introduce a change that become fixed in the DNA sequence.