Having forged a relationship from playing against one another the past couple of years, they have exchanged flattering words throughout the NBA's Western Conference finals, had dinner together earlier in the series, and even faced off in Game 2 while Williams' wife Amy sat with Parker's fiancee, actress Eva Longoria.
But on the court?
Williams and the Jazz hate the way Parker and the Spurs have killed them by driving too easily to the basket - something that ranks as their most pressing concern heading into Game 3 of the best-of-seven series at EnergySolutions Arena on Saturday.
"We can't win if we don't get stops," Williams said.
That was the overwhelming sentiment among the Jazz at practice Thursday, after allowing the Spurs to shoot nearly 55 percent (including 48.6 percent from three-point range) in winning the first two games of the series in San Antonio. And Parker is the primary problem, having been able to use his blinding speed to get past Williams and slash into the lane.
"Layups is killing us," forward Andrei Kirilenko said.
It's not only layups, though.
While the Spurs have enjoyed their share of those - 102 points in the paint, in two games - they also have hit the jump shots and three-pointers that have opened up when the Jazz have collapsed their defense into the lane in an effort to stop Parker and similarly slashing teammate Manu Ginobili.
The Spurs made a franchise playoff-record 13 three-pointers in Game 2, for example.
"Literally, the bottom line is we have to pick it up defensively," the Jazz's Carlos Boozer said. "I mean, I know there's a million things you could talk about offensively - guys aren't stepping up, blah, blah, blah, blah. Bottom line is, our defense has to be better. I mean, the numbers are retarded. They're shooting 50 percent for three, they're shooting almost 60 from two. I mean, they're scoring too easy and too well."
Much of that is because of Parker.
He's almost the exact opposite of Golden State's Baron Davis, against whose strength and physical style Williams strained but ultimately prevailed in the Jazz's previous playoff series. And while Parker and teammate Bruce Bowen have not been able to stop Williams when he has the ball - Williams has averaged 29 points in the series - nor has Williams or anybody else been fast enough to impede Parker.
Davis "is more one-on-one moves - crossover, crossover, crossover, you know, to set up his move," Williams said. "Tony don't have to do that. Starts right there" - Williams points to the top of the key - "and takes off. If he don't have you, he'll back up, and go the other way. He's just faster. It's so hard to stay in front of the guy, no matter what you do. I'll be looking for a screen-and-roll, I'll turn my head to look, see if it's coming this way? As soon as he sees me look, he's gone. His first step is unbelievable."
Curiously, it's the screen-and-roll - that age-old cornerstone of their own offense - that is hurting the Jazz the most, they said. That's one reason unheralded centers like Fabricio Oberto and Francisco Elson also have enjoyed such success against the Jazz in the series.
"We have to be a little bit more determined to try to stop them," coach Jerry Sloan said.
Especially in the second quarter.
The Jazz are still trying to figure out why they have melted down in that period in each of the first two games, scoring a franchise playoff-low 16 points in Game 1 and improving by just one point in Game 2. Both times, the Spurs took advantage of the lulls - they scored 31 and 32 points in the quarter, respectively - to essentially bury the Jazz.
"It seems like they're all on the same page, and they're reading the same book at the same time," Boozer said. "And on our team, it seems like some guys are on page 23, some guys are on page 18. If we can get all our stuff on the same page like they are - and we do that, for about three quarters; that second quarter has been kicking our butt lately - if we can have everybody reading the same page in the second quarter, I think we'll have a good chance."