The coaches, Bill Belichick and Tom Coughlin, again will have an Xs-and-Os duel. The quarterbacks, Tom Brady and Eli Manning, once more will battle for passing supremacy. It will be a highly anticipated Super Bowl rematch when the New England Patriots and New York Giants square off here Sunday evening at Lucas Oil Stadium.

But it’s not really a rematch at all. The cornerstones of these teams — Belichick and Brady for the Patriots, Coughlin and Manning for the Giants — remain from the memorable game four years ago. But the casts on both sides are mostly different, and this Super Bowl is better understood as a testament to each organization’s ability to retool around its coach and quarterback and return to pro football’s pinnacle.

“There aren’t that many people who played in the last game four years ago,” Belichick said last week. “This team is this team. . . . This game, the elements of it, are what we have in front of us, not what happened two months ago or what happened two years ago or four years ago.”

Only eight Patriots players remain from the 2008 Super Bowl, when the Giants wrecked New England’s perfect season. That modest total includes center Dan Koppen, who is on the injured reserve list. The Giants still have 15 players who played in that game.

But as one of them, running back Brandon Jacobs, said: “That’s gone. This is a new year.”

Making tough decisions

Only two of Brady’s teammates, left tackle Matt Light and running back Kevin Faulk, have joined him for all five Super Bowl appearances in this dynastic run. Belichick has been willing to make the difficult, unsentimental decisions necessary in the salary cap era, and he has remade and reinvented the Patriots over and over again.

Four of the Patriots’ holdovers start on offense: Brady, wide receiver Wes Welker and the left side of their offensive line, Light and guard Logan Mankins. Wideout Randy Moss, a dominant receiver in the 2007 season, is gone, and the Patriots have reshaped their offense to emphasize the talents of tight ends Rob Gronkowski and Aaron Hernandez, who arrived together in the 2010 draft. On defense, the only starter remaining from the Super Bowl four years ago is defensive tackle Vince Wilfork.

Belichick is known as a defensive guru. Yet this Super Bowl title, if the Patriots capture it, would be built around Brady’s passing. New England’s defense ranked 31st in the league during the regular season.

Belichick likes to stockpile draft choices, and the Patriots guess right on many of the picks they use. They famously selected Brady in the sixth round of the 2000 NFL draft. He is among the 24 players on the current 53-man active roster originally drafted by the Patriots. But New England also has experienced draft-day misses, for which the organization compensates by finding under-appreciated talent and getting the most out of the group it assembles. Of the 53 players on the roster, 18 originally entered the league as undrafted rookies.

Welker, who ranked second in the NFL in receiving yards this season, arrived via trade with the Miami Dolphins after he was waived by his original NFL team, the San Diego Chargers, and revived his career in Miami.

“I tell the team that I don’t care how you got here,” Belichick said. “It’s what you do when you get here. It doesn’t matter if you were drafted in the second round, the fifth round or not drafted at all. Ten years in the league [or] one year in the league — we are going to play the best players.”

Brady said several times over the past week that Belichick coaches him, even now, as he did when Brady was an unproven rookie.

“There really is no separate treatment for different players,” Brady said. “The rookies are expected to perform and act the same as the veteran guys. It’s great as a player on our team because . . . you really don’t have to hold the other players accountable, because the head coach does it. He’s very tough. He says to us from time to time he understands that it’s a demanding place to play and that it’s really not meant for everybody.”

A slightly different approach

The Patriots are back in the Super Bowl for the first time since their loss to the Giants, their longest stretch without an appearance since they secured their first Lombardi Trophy at the end of the 2001 season. The Giants have not been as consistently superb. But if Coughlin and Manning collect a second Super Bowl title, it would not be difficult to envision their tickets to Canton, Ohio, for Hall of Fame enshrinement eventually being punched.

Whereas Belichick is the key decision-maker on football-related matters for the Patriots, the Giants have a general manager, Jerry Reese, charged with assembling the roster that Coughlin coaches.

“We’ve always been a traditional organization where you have a general manager and a head coach,” Reese said. “You have slots and that hierarchy. It has always been that way with the Giants.

Two of the Giants’ standouts from the 2008 game, wide receivers David Tyree and Plaxico Burress, are long gone. Manning now has two 1,000-yard wideouts, Hakeem Nicks and Victor Cruz. Running backs Ahmad Bradshaw and Brandon Jacobs still are around and the offensive line has been tweaked, not overhauled. Pass rushers Osi Umenyiora and Justin Tuck remain but Jason Pierre-Paul has replaced the retired Michael Strahan.

The Giants signed Cruz, who ranked third in the league in receiving yards this season, after he went undrafted out of the University of Massachusetts.

“We had Victor Cruz ranked just like everyone else: We had him ranked as a free agent, and he was a free agent,” Reese said. “He has surpassed all of our expectations with respect to what he has done. That happens. In scouting, it’s not a perfect science. Every now and then, you get lucky with guys like that.”

Good luck certainly is part of it. But the bigger part of the successful team-building equation appears to be stability, which Giants co-owner John Mara called the key element for the league’s most successful franchises. What the Giants and Patriots have demonstrated is that if the pillars remain in place at coach and quarterback, a team has at least a chance to put the other championship pieces in place.

Mara recalled that when he shook Belichick’s hand in the tunnel after the Patriots beat the Giants in the 2007 regular season finale, Belichick told him the two teams would play again. Mara remembered being somewhat skeptical at the time about the Giants’ chances to do their part in making that prediction come true, but weeks later Belichick turned out to be right.

And when Belichick, once a Giants assistant coach, called late in this regular season to offer congratulations for a win, Mara said, Belichick made a similar prognostication.

“He said, ‘We’ll play again,’ ” Mara said. “So, again, I think that was met with the same bit of skepticism. But he turned out to be right.”