They come from the same coaching tree, disciples of Bill Parcells. That and a no-nonsense approach are what Tom Coughlin and Bill Belichick have in common.

Otherwise, the men who have done some of their best coaching to get their teams to next Sunday’s the Super Bowl are very much opposites. Coughlin, the offensive guru, is demonstrative on the sideline, his face getting redder with every snap. Belichick, the defensive mastermind, is stoic, unemotional, seemingly detached — even as he manipulates everything from under his hoodie.

The players take after their coaches, too. The Patriots follow Belichick’s never-say-anything-revealing lead; the Giants tackle tough questions with verve.

Eli Manning, who has flourished under Coughlin’s tutelage and now must be ranked among the game’s elite quarterbacks, says the Giants not only appreciate Coughlin’s style, but become better players because of it.

“Just the way he prepares, the way he gets his team ready, his messages.” Manning says. “The way his attitude is portrayed onto the players and the players kind of take on that attitude in their preparation and approach to play.”

Coughlin once was almost unapproachable, so set in his ways that players feared him more than respected him. That changed before the 2007 season, when a group of Giants veterans asked him to “loosen up,” as Michael Strahan, then a star defensive tackle, described it. They believed Coughlin’s intense, even relentless approach caused friction throughout the team.

To his credit, Coughlin saw the merits to opening up, did so, and the Giants went on to win the Super Bowl, shocking the 18-0 Patriots for the championship.

Coughlin showed his sense of humor during the buildup to that game when asked if, because the Giants were stronger defensively, would they consider kicking off to New England’s record-setting offense if they won the coin toss?

“What,” he said with mock astonishment at the prospect, “and give them one more time with the ball?”

By all accounts, the 65-year-old Coughlin has gotten even looser the last few years.