While Jay Leno and Jimmy Fallon were occupied trying to put the best possible face on NBC’s latest “The Tonight Show” baton pass Monday, the night’s best line actually belonged to David Letterman. Leno was in his last week as host, Letterman noted, and the Winter Olympics were about to begin: “Two events that happen every four years.”

Across the dial, Leno sounded mildly nostalgic — talking about this week’s lineup of guests, and saying not to submit any more “Headlines” — before bringing out Fallon, engaging in light banter about the comic’s young child and reminiscing about Fallon’s first “Tonight Show” appearance.

Everyone was gracious, if a little stiff and stilted — and finally, sappy. Closing with his “thank you” bit, Fallon thanked Leno for his “humor and class … and for being nothing but gracious and generous to me over the past years. I will do my best to make you proud every single night.” For his part, Leno made it sound like he was pleased as punch to see Fallon slide into “The Tonight Show” seat that, he recently told Variety, is bigger than any of its occupants.

The only problem, for those who bother to remember such things, is history. Leno has insisted that he’s much more serene about leaving this time around, in part because NBC officials were more solicitous, and in part because he sees Fallon as such a worthy replacement.

Yet the parties all tried to convey precisely the same image five years ago, when Leno handed the reins to Conan O’Brien. And the only person who came away from that interlude happy was the New York Times’ Bill Carter, who got another book out of it.

Leno has stated that he has no interest in hosting another latenight program, but other than a vague reference to being flattered to receive feelers, he hasn’t cemented any plans. And because he’s not the kind of a guy to sit idly on the beach, the network is going to have sweat out the transition for a while, waiting to see if club dates and a lesser TV workload will be enough to keep Leno satisfied in his golden years.

Obviously, NBC is going to consume a lot of oxygen over the next several weeks between Leno’s official exit, the Olympics and Fallon’s debut, but keep an eye on Letterman. Having battled Leno all these years — and helped send O’Brien packing to basic cable — he might have his own push to the finish line, as well as the advantage of nothing left to prove, or lose, beyond a competitive longing to go out on top.

So while Leno might be packing in that old “Headlines” routine, the ones that will really tell the next chapter in the latenight story won’t be written until some time after the “Tonight” torch has been passed — and the Olympic torch has been extinguished.