Aidan Pilkington was killed on Crow Road in the Jordanhill area of Glasgow early on Saturday, while three women and two men were taken to hospital after being hit by a car in Rose Street in Edinburgh city centre early on Sunday.
Police announced on Sunday night they had traced the car which hit Mr Pilkington while it was travelling southbound on Crow Road near Woodend Drive at around 12.20am on Saturday.
A 19-year-old man has been arrested.
Mr Pilkington was taken to the Queen Elizabeth University Hospital but was pronounced dead.
His family said: "Aidan was treasured by his family, and well loved and respected by his friends and community.
"Aidan left Hyndland Secondary School in the summer, and was going to be moving to Dundee next Saturday to attend Dundee University.
"He created a bright future for himself and was really looking forward to these opportunities and challenges.
"It is very cruel that he has been robbed of his life in this way.”
Staff at a nearby branch of the McDonald’s burger chain where he worked set up a fundraiser for his family which had raised nearly £7,000 by Sunday.
Sergeant Scott Sutherland of Police Scotland’s road policing unit, said: “The car involved has now been traced, and a 19-year-old man has been arrested in connection with this incident.
"He’s been released pending further investigation.
“We would like to thank everyone who has got in touch with us so far regarding the appeal, and urge anyone who has information, but has yet to contact us, to call 101 quoting incident reference number 0120 of 11 Sept 21."
In the Edinburgh incident, the pedestrians were hit by a car in Rose Street – much of which is a pedestrianised zone – before it collided with a bus on Lothian Road.
Police said the injured were in a stable condition in hospital.
A 36-year-old man has been arrested in connection with the incident.
It is understood it is not thought to be terror-related or otherwise targeted, or linked to a medical condition.
A Police Scotland spokeswoman said: “Around 12.40am on Sunday, we received reports of five pedestrians being hit by a vehicle on Rose Street near its junction with Frederick Street in Edinburgh.
“Two men, aged 39 and 60 years old, and three women aged 37, 22 and 65, were taken to Edinburgh Royal Infirmary for treatment where they all remain in stable conditions.
“The vehicle did not stop at the scene and continued to Lothian Road where it was involved in a crash with a bus.
“No further people were injured.”
Lothian Road remained closed on Sunday as far south as its junction with the West Approach Road.
June Ross, who set up the Don’t You Forget About Me support group for victims of road traffic incidents following the death of her son Ian, 22, in 2010, told The Scotsman: “These are both awful scenarios.
"My heart goes out to the 18-year-old’s family on their tragic loss and I hope all the Edinburgh injured will recover, as it’s the mental as well as the physical trauma.”