Your question made me curious so I browsed the handbook. A child under 8 can be a 'member of record' but the question is whether or not they are 'a member'. The handbook always uses the phrase 'member of record' for children under 8. A baptized member of any age is also a 'member of record'. But, is vice versa true? For example, would an unbaptized teenager of a baptized member that is a 'member of record' also be 'a member'?
18.2.2.8 - Introducing New Members
https://www.churchofjesuschrist.org/stu ... ng#title13
When membership records are received in a ward and when converts are baptized and confirmed, a member of the bishopric introduces and welcomes the members in the next sacrament meeting. He reads each person’s name, invites the person to stand, and asks members of the congregation to show by the uplifted hand that they accept the members in full fellowship in the ward. Records of family members are read together. If a member knows any reason why a person may not be entitled to full fellowship, he or she should talk to the bishop privately.
After children who are members of record are baptized and confirmed, a member of the bishopric announces each child’s baptism and confirmation in sacrament meeting. These children are not presented for acceptance into the ward because they are already members.
This may mean they are already members of the ward or it could be read that they are already members of the church. But if it meant the latter, then why would you read in moved in members in the ward since they are already members of the church too?
I'm overthinking it too.