Stephen Curry’s favorite memory of playing against LeBron James isn’t from any of the three championships he won with the Golden State Warriors against James’s teams. It was from his 2009-10 rookie season, when James was in his seventh year with the Cleveland Cavaliers.

They first met when James attended one of Curry’s college games for Davidson. The night before their first N.B.A. clash, in Cleveland, James hosted Curry at his home.

“For me, as a rookie, it was a whirlwind of excitement,” Curry said. He added: “The fact that he’s as big as he is, as strong as he is, as skilled as he is, there’s never a time he can’t get a shot off.”

James scored 31 points, most coming from near the rim or at the free-throw line. He hit just one 3-pointer.

More than a decade later, James’s game looks different, though he can still dunk as if the rim insulted his honor. The N.B.A. has evolved rapidly since James entered the league in 2003, and his ability to change with it helped him break Kareem Abdul-Jabbar’s seemingly unbreakable career scoring record of 38,387 points on Tuesday. James has 38,390 points now.

“Nobody could imagine somebody doing it,” said Drew Gooden, who played hundreds of games alongside James in Cleveland. He added: “If you would have said or told somebody in 2003 when LeBron James got drafted when he was 18 years old that he was going to break Kareem Abdul-Jabbar’s scoring record, they would have looked at you like you were crazy.”

N.B.A. Commissioner Adam Silver, in an email, called the record “one of the most hallowed” in all sports. Of James, he said, “His extraordinary athleticism, power and speed leave you in awe.”

Over the past 20 years, James’s ascent to the top of the scoring list has impressed Hall of Fame players as he made a definitive case to join their ranks and perhaps be considered the best among them. His shots have felled the toughest competitors, yet made them fans as he blocked them from fulfilling their sports dreams. His teammates have amassed stories of the joys of playing with him — and the pain of being on the other side.

At 38, James is one of the N.B.A.’s oldest players. He’s also still one of its best.

“It’s not like he’s holding on for dear life just to get the award,” Curry said. “He’s still playing at a high level. So it’s pretty damn impressive.”

Abdul-Jabbar, 75, played in the N.B.A. from 1969 to 1989 after starring for three seasons at U.C.L.A. When he broke Wilt Chamberlain’s career scoring record in April 1984, he did so with his patented, and nearly unstoppable, shot: the sky hook.

James hasn’t cultivated that kind of signature.

“Now, is there a shot that you know that he got that would make you say LeBron James? No,” said George Gervin, 70, a Hall of Fame player who won four scoring titles and is known for his finger roll.

Instead, Gervin said, James’s “greatest attribute will be his ability to be consistent.”

James has methodically developed his game all over the floor, borrowing from the greats. During any given game, he might shoot the fadeaway from the post perfected by Michael Jordan and Kobe Bryant, go for a logo 3-pointer like Curry or do the “Dream Shake” he was taught by its namesake, Hakeem Olajuwon.

“LeBron has scored baskets in every way possible,” Philadelphia 76ers Coach Doc Rivers said.

Rivers, who has also coached the Orlando Magic, Boston Celtics and Los Angeles Clippers, said he recently ran into James in Los Angeles and joked, “I think you scored at least 10,000 of those points against one of my teams.”

He said James responded, “‘Those Celtics points were the hardest damn points that I’ve ever had to score.’”

Defenders became “more fearful” as James expanded his game, Rivers said.

“When LeBron first started, you wanted to take away his right hand. His drive. His attacks to the basket,” Rivers said. “You actually would sag off and give him shots. Then he started going both ways with the ball, which made it more difficult to guard. Then he got the in-between game.”

The Miami Heat’s Bam Adebayo, one of the league’s best defenders, said James was “like a computer.”

“He’s calculating everything that is going on at a rapid speed,” Adebayo said. “So it would be like you typing normally and you got somebody on, like, Excel saying it to the computer and the computer is just reading what they’re saying and just typing it.”

James is known for his savvy, but also for his strength.

“His area of attack is at the top of the floor,” said Mike Brown, who coached James for five seasons in Cleveland. “Everybody knows it, but nobody can stop it.”

Diana Taurasi, who holds the W.N.B.A.’s career scoring record, said James was “probably still the most dangerous man in transition.”

Gooden said he “took it for granted” that he had played with James. That is, until 2008, when Cleveland traded Gooden to Chicago and he tried to make the Cavaliers regret it the first time he faced off with James.

“I jumped right in LeBron’s way, and it was like a freight train hit me,” Gooden said. “He came across with two elbows. All his elbows went across my face. Basically, he got an and-one. And I came out of the smoke with a bloody, busted lip. And I was like, ‘Wow, that’s what everybody’s been having to deal with.’”