Oak Island Mayor Betty Wallace told CNN that the female swimmer was attacked first, around 4:15 p.m. Less than 90 minutes later, as responders were still tending to her, the boy was attacked.
It is not typical to shut down the beach or evacuate the water after a shark attack, town spokesman Kyle Thomas said.
Both victims were airlifted to New Hanover Regional Medical Center in Wilmington. Both arrived in critical condition, according to hospital spokeswoman Martha Harlan.
Harlan said each has had an arm amputated -- his below the shoulder, hers at the elbow. The girl also sustained serious tissue damage to her leg, according to Harlan.
Both patients -- whose names are not being released -- have since been upgraded to fair condition.
Wallace told CNN that shark attacks are so rare at Oak Island -- a beach town on the state's southernmost coast -- that she couldn't remember one occurring before Sunday.
Witness Jason Hunter told CNN affiliate WWAY
that the shark involved in the attack on the boy was 7 or 8 feet long.
Both incidents occurred at high tide in the vicinity of Ocean Crest Pier, a popular destination among beachgoers.
"At the pier this time of year, I'm sure the beach was packed," said Wallace.
The pier is also a popular spot to fish from, meaning there was likely bait in the water that could have attracted sharks.
A 911 call released by Brunswick County captured the drama of the first attack.
The dispatcher tells the caller, "we're getting help on the way. Are any of the fingers completely amputated?"
The response: "It looks like her entire hand is gone,"
Marie Hildreth, an off-duty EMT, happened to be vacationing at the beach, and ran to provide aid after hearing someone yelled "shark!"
Seeing that the girl was hemorrhaging, Hildreth decided to put tourniquets on two different limbs, she told CNN's Anderson Cooper.
She used what was available: a string from a boogie board and a string from a tent.
One of the first on-duty paramedics at the scene, Tracy Carnes, credited bystanders' help for saving the girl's life.
"The outpouring of help from the bystanders was amazing," she told CNN's Erin Burnett. "The tourniquets were in place by the time I got there."
The Oak Island beaches remained open on Monday, but in contrast to most summer days, virtually no one was in the water.
The beach was not empty, but nearly everyone stayed on dry land.
This area, which has mostly houses and no highrises, does not attract the throngs of visitors that more touristy beaches do. It's mostly a haven for families who come and rent houses and enjoy the beach. But even by local standards, the beaches on Monday were quite desolate.
Helicopters from the sheriff's office monitored the coastline.
Oak Island, south of Wilmington, is home to about 7,000 residents, but tourists swell the population to about 25,000 during the summer, Anselmo said.
About four or five people are bitten by sharks on North Carolina beaches each year, said George Burress, an ichthyologist and fisheries biologist with the Florida Museum of Natural History. The incidents usually involve smaller sharks, he said.
"Having a series of injuries so close to each other in time and space makes this unusual," he said. "Two in one day very close to each other suggests that there's a focused problem. It might suggest a single shark has been involved."
He suspects the predator could be either a bull or tiger shark, both of which are undaunted by larger prey, he said.
"They may have interpreted the humans as being appropriate in size and behavior to give it a shot," the researcher said.
Only three times in the four decades that he's been studying sharks has Burgess seen attacks happen "so closely in time and space," he said. The other incidents occurred in Egypt and Florida.
Any number of factors, including an abundance of fish or nesting turtles, could draw sharks to the area, Burgess said.
Burgess urged people to remember that despite the horrific nature of Sunday's attacks, shark attacks are unusual. Last year saw 72 attacks, only three of which were fatal, he said.
"Considering the billions of hours we spend in the sea," he said, "it's clear that shark attacks aren't common."