PARIS—They labored under suddenly friendly skies here in Paris today, separated by a distance that could almost be covered by a good offensive lob. Rafael Nadal was dismantling Stanislas Wawrinka on Court Philippe Chatrier, while over in Suzanne Lenglen, Novak Djokovic was laying a hurt on the closest thing the tour has to a senior citizen, 35-year-old Tommy Haas.

Each man was a little too busy paying attention to the task at hand to think much about the other, but in their own ways Nadal and Djokovic were rushing headlong toward a destiny that nobody needed to articulate—a semifinal match Friday at Roland Garros, in the latest installment of the rivalry that has come to dominate the tennis headlines.

Djokovic handled Haas with workmanlike precision despite a few lapses, none of which proved particularly dangerous. Meanwhile, over on Chatrier, Nadal was hellbent on squeezing every potential bit of confidence for Friday out of the hide of Wawrinka. Nadal has been chasing “improvement” here like a dog chasing its tail. The difference is that Nadal sometimes catches his.

Djokovic, the top seed, gave up 14 games and had to navigate a tiebreaker before he won in straight sets. Nadal allowed Wawrinka just six games in a 6-2, 6-3, 6-1 win that lasted under two hours. Djokovic took 17 minutes longer, and quit the court eight minutes after the last wave of applause on Chatrier washed down over Nadal.

That left the men in a good position to go out to dinner together, although it’s more likely that they’ll spend the night huddled in a dark closet in their respective hotel rooms, sticking pins into voodoo doll representations of each other.

Neither man likes to delve too deeply (or, at the very least, too publicly) into the psychological conflicts that underlie this rivalry; each of them likes to play it cool. For what it’s worth, though, Djokovic won the battle of the press room. He looked relaxed and comfortable as he fielded questions, sparred playfully with a few of his interlocutors, and said of the pending clash:

“I look forward to it. You know, it’s not the first time I’m playing him. We played over 30 times. I’m sure that we know each other’s game really well. . .This is it, you know. This is the biggest matchup of our Roland Garros 2013 campaign for both me and him. I guess it’s the small details and few points that can decide a winner, and that’s why I need to be very disciplined and focused in order to get emotionally, physically, and mentally ready for that match.”

Djokovic praised Nadal’s “love of the sport” and told us how Rafa’s unyielding nature is an impressive virtue that inspires his respect. He also fired a shot across Nadal’s bow when he declared that he’ll take some confidence into Chatrier when the time comes, a residual benefit from his impressive, straight-sets (6-1, 7-6 [1]) win over Nadal a few weeks ago in Monte Carlo.

“That is something that can maybe give me that mental edge when I step onto the court,” Djokovic suggested. “That knowing I already won against him on clay this season, knowing I can do it, even though not many players in last ten years have won against him on this surface, and he’s been the most dominant player in the history of this sport on this surface.”

As for the X’s and O’s, Djokovic downplayed the notion that the match will turn on the efficacy of his backhand (which in some quarters is the conventional wisdom) and chose a more holistic approach. “It’s not only about that shot, but everything has to work in harmony. Everything has to be synchronized and you can’t have many ups and downs throughout the match. . . I know what it takes to win against him and that’s what I’m going for. I’m going to win. That’s the mindset.”

By contrast, Nadal looked twitchy as a jackrabbit in coyote country when he came to visit with us. Before you Djokovic fans start punching the air, keep in mind that Nadal tends toward the jumpy at the best of times. But you know with this guy that when his brow is furrowed and his left eyebrow leaps up to form a crescent above his eye, he’s busy trying to work something out in the back of his mind. And that eyebrow was raised for almost the entire interview. His words came out at intervals, as if he were shutting a faucet on and off, and that familiar, pained smile constantly flickered across his elastic features.

Nadal made an effort to disabuse us of the notion that we are about to witness Armageddon: The Sequel, come Friday. He reminded us: “It is not the finals; it’s the semifinals. That’s the difference at the end. You are not playing a match for a title. You are just playing a match to be in the final. So is a big difference. Sometimes it’s a little bit strange, but that’s how my mentality sometimes works.”

As for Monte Carlo, Nadal had had a salvo of his own to fire. “Every match is different history,” he reminded us. “We’re going to play here in Roland Garros; we’re not in Monte Carlo. This court, and the feeling to play this court, is always a little bit different, I will say.”

But Nadal added a disclaimer that softened his warning: “I know he’s going to play well too because he’s the best today, and I hope to play well here.”

That sounded no more convincing to me here in Paris than it does to you at home. Sometimes, it must be hard for these guys to take the high road that has become the route of choice in this collegial era.

But don’t let Nadal’s equivocation fool you. After all, as the seven-time French Open champion he’s entitled to feel a little jittery; nothing this great lasts forever, although on the evidence the juggernaut hasn’t slowed yet. That was clear in Nadal’s match with Wawrinka, which represented a significantly better performance than he delivered in his previous matches. Wawrinka played well, he even threatened a few times. But Nadal slammed the door shut. So if Djokovic won the battle of the press room, Nadal had a slight edge in the war on clay.

For days now, Nadal has stressed that he needs to get better. He feels he’s accomplished that goal. He said his rivals have spurred him in this quest to improve even as the sands were running through the hourglass.

“I made the improvement against Nishikori (in the previous round), and today I made another important improve. In my opinion always I played at a very good level (today). To win against a player like Wawrinka is impossible with this score if you don’t played at a very good level.

So take your pick: The guy treading water, externally calm and confident, or the fella who’ll go to sleep tonight feeling he’s peaking, that all the pieces are falling into place once again at the place where he’s solved the most complex of those athletic jig-saw puzzles. It may not be Armageddon, The Sequel, but it doesn’t feel much like just another semifinal, either.

Follow the Nadal/Djokovic semifinal with us during a live chat on Friday at 7 am EST.