The description of the vehicle is different in both cases, Detective Senior Sergeant Brett Batty said.
Police are investigating whether the incidents are linked.
"The motives of the person or persons involved may well be innocent but it is timely to remind people that these sorts of offers, though done with the best of intentions, can often be misconstrued," Mr Batty said.
"We are keeping an open mind on these events."
The cases at Red Beach follow an incident on Greenhithe Rd, about 24km from Red Beach School, which is not believed to be linked.
On Monday a 5-year-old boy was approached by a suspicious man as the youngster walked home about 50m in front of his mother.
Detective Sergeant Megan Goldie said a man in a white van approached the boy, who was able to "wriggle away".
Ms Goldie said police were attempting to clarify what had happened and were yet to properly interview the boy, who required an interpreter because of language differences.
The man has been described as Caucasian, aged in his 40s and with curly brown hair and a possible limp.
There have been multiple calls from people who believe they saw something suspicious at the time or know a person who may be a suspect, Ms Goldie said.
Police are investigating if any of the businesses on Greenhithe Rd caught the incident on CCTV cameras.
"Members of the public have been really helpful in assisting police with inquiries and providing information to police," Ms Goldie said.
Mr Batty said it was fortunate that the man offering a lift to young girls at Red Beach had been "firmly rejected".
"Police spend a considerable amount of time in our schools teaching children how to keep safe. In this case I am glad to say that these lessons have resonated and have been acted upon," he said.
Anyone with information should call Crime Stoppers on 0800 555 111.
