Harley Watson suffered fatal injuries and six others, including five pupils, were hurt when the silver Ford Ka mounted the pavement by the school in Loughton, Essex.
Horrified parents saw children “flung into the air” outside Debden Park High School at 3.30pm on Monday.
Harley was treated by paramedics at the scene but later died in hospital.
Detectives are also investigating reports of a car mounting the pavement outside nearby Roding Valley High School just minutes earlier.
They have now ruled out any connection to this separate incident in Loughton at around 3.10pm on the same day.
Police established that the incidents involved different vehicles and drivers of different descriptions.
A 51-year-old man was arrested after the Debden Park High School collision and remains in police custody on suspicion of murder, six counts of attempted murder and one of causing death by dangerous driving.
He is also accused of six offences of causing serious injury by driving, failing to stop at the scene of a collision and driving without insurance.
Two 15-year-old boys, a 13-year-old boy, a 16-year-old girl, a 12-year-old boy and a 23-year-old woman were also injured.
A fundraising campaign for Harley’s family raised almost £53,000 since it was set up on Tuesday .
A post on the Gofundme page read: “Loughton and Debden residents stand united to support you all [Harley’s family] through this difficult time and offer our sincere condolences to everyone involved in this heartbreaking incident which has shocked the community.”
“Harley was a good, kind, helpful and lovely boy. We would like to thank everyone for their kind wishes and concern. However as a family we would like people to respect our privacy and allow us to grieve in peace.”