Last Saturday, the Toronto Maple Leafs won the 2016 NHL Draft Lottery, giving them the top pick and the chance to select Matthews in June.
One year ago, McDavid was playing for Erie in the Ontario Hockey League playoffs, knowing the Edmonton Oilers were likely to take him with the first pick.
"It's a fun experience," McDavid said after they faced each other for the first time in a 5-1 win against the United States on the first day of the 2016 IIHF World Championship, "but there's a lot of pressure that goes with that, and a lot of attention. I'm sure he's trying to do the best he can, trying to enjoy it."
Like McDavid, Matthews is a center who is expected to be a franchise player in the NHL. But the two players are defined as much by their differences as by their similarities.
McDavid was raised in Toronto and learned his craft, like many elite players who came before him, in the OHL. Matthews was born in San Francisco and raised in Scottsdale, Ariz., and will be the first No. 1 pick from Arizona if the Maple Leafs call his name June 24.
Matthews is 18, but at 6-foot-2, 194 pounds, he already has a man's body, which helped him finish 10th in scoring in Swiss National League A in 2015-16 with 46 points in 36 games for Zurich.
After being out of the spotlight in Europe for most of his draft year, Matthews has a great chance at the World Championship to show NHL teams how he measures up against established players in the League.
Neither McDavid nor Matthews made an impact on the score sheet Friday, but Matthews made a strong impression on his teammates and on his opponents, many of whom were seeing him play against professionals for the first time.
"He's a bigger body than I expected," Montreal Canadiens forward Brendan Gallagher said.
"He's hard on the puck, good on draws and all that," Oilers forward Taylor Hall said.
Maple Leafs defenseman Morgan Rielly, well aware that he could be talking about a future Toronto teammate, said, "There were some moments where he had the puck on a string and was able to make some plays, create some offense. But I think more than that, he was a good two-way player. He was responsible, managed the game well. I think he's got a bright future.
"Whether he gets drafted by Toronto or not, we'll see. But he's a great player."
There's one other significant difference between Matthews and McDavid: After scoring more than a point per game as an NHL rookie (48 in 45 games), McDavid has already secured a roster spot at the World Cup of Hockey, which runs from Sept. 17-Oct. 1 in Toronto.
McDavid, 19, was one of 16 players named to the intial roster for Team North America, a group of Canadian and American players born on or after Oct. 1, 1992. The timing of the World Championship offers Matthews an opportunity to impress Team North America general managers Peter Chiarelli and Stan Bowman, and earn one of the final seven spots on the roster, which will be finalized June 1.
Forward Pat Maroon, who plays with McDavid on the Oilers and started the World Championship playing on Matthews' line, said Matthews is "a very special player."
"I'm not the coach, I'm not the GM of whoever he gets drafted by," Maroon said. "But as a player, playing with him, yeah, he's got NHL upside to him. He's a gifted player. That's just the nature of how people are born. Some people have it, and he has it."