The film is at odds with itself as to whether this is Sarah Ann Connor or Sarah Louise Connor.
If the killing of this character is indeed the Terminator's first target (assuming he is going by the order in which they appear in the phonebook), this would be Sarah Louise Connor.
The first television report simply says that it is "Sarah Connor, 35, mother of two". But at the police station, Vukovich tells Traxler that Sarah Ann, 35-year-old secretary and mother of two, was shot six times (as shown in the earlier scene).
Then, the later television report says that Sarah Ann, 35, was killed in her apartment, and implies that the "Wrong Sarah" is Sarah Louise Connor.
Additionally, the house number of this Sarah, 14239, corresponds with none of the addresses listed in the phonebook.
It is probable that her two children were not harmed by the Terminator because, having detailed files, he would have known John Connor's birth date was roughly nine months in the future. Though it is also possible, that the Terminator, being a systematic machine would wipe out any offspring connected to the Sarah Connors, since it doesn't discriminate between humans and kills them all the same.