The title is only slightly clickbait-y but let me cook.
To start, we know for a fact that Shanks and Kaido met prior to Marineford in the New World.
The Main Evidence
According to King's vivre card, King came with Kaido but was stopped by the Red Haired Pirates. This confirms that Shanks was with his crew, and that King was with Kaido, but nothing is mentioned of Queen or anyone else so it can be reasonably assumed that Kaido and King alone were up against the Red Hair Pirates in this scuffle. The anime supplements this saying there was indeed a conflict that happened, even if it was a small one. The result of this scuffle was that Kaido was stopped.
2 years later:
Roof Piece
Kaido thinks of 5 strong pirates capable of fighting him. Shanks is counted among these five. Now who are the other four, and what have they done to get Kaido's respect, which is obviously based around strength?
Well, to start, we have the three strongest pirates in history: Rocks D. Xebec, the Pirate King Gol D. Roger and Edward Newgate.
The Kings of Eras
Kaido was a freak even as a teen, but Rocks brought him under his wing, just another strong member of Captain Rocks' great Pirate Crew. Rocks is an absolute menace who only lost when he fought Roger and Garp at God Valley, presumably with the Roger Pirates in tow. Up to that point, Rocks was the name of the era, and implications to date imply that he was every bit as strong as Roger was, and undoubtedly stronger than Kaido at that time.
After the Rocks Pirates disbanded, Roger just kept rising and rising until he eventually became the Pirate King. The very first panel of the series speaks of Roger's power, and every old legend is held to his standard, so it is abundantly clear that Roger was at the peak of power among pirates. During Roger's era, Kaido had started to take over Wano, and other than that, his exploits with big name pirates between God Valley and Roger's death aren't that well known. We can reasonably assume that Kaido was never at his peak when Roger was around and that he at least saw Roger's power first hand on God Valley.
With the end of Roger came the Golden Age of Pirates, where people wanted the One Piece but ultimately didn't stand a chance because Whitebeard was still around, sitting in front of the throne, the de facto Pirate King who didn't care for the title. Renowned as the World's Strongest, the aging and sick Whitebeard was the king of the seas until he came to Marineford and died at the hands of the Marines and Blackbeard Pirates, bringing in the New Age with his final words. Kaido was in Wano this entire age except for some expeditions, but it's unlikely that he ever fought Whitebeard after Roger's death since Whitebeard was known to have been quiet before Marineford. Only after Whitebeard's death was the throne truly open for the taking.
Whitebeard's legend
Because of this, I call Rocks, Roger and Whitebeard the Kings of Eras. From Rocks' reign to Whitebeard's death, there was a clear top dog, and only after they all died was a true free for all able to take place in the world. It's abundantly clear that their raw strength, regardless of their crews, is on a completely separate level from any other pirate, including Kaido. All three of these Kings are above Kaido and enjoy a comfortable spot in Kaido's "top 5," likely due not only to their legendary reputations but the strength that Kaido knew they had, as he was personally familiar with them all up to at least God Valley.
The fourth pirate Kaido thinks of is the samurai, Oden. As far as we know, Kaido only ever had one single fight with Oden, which resulted in Kaido gaining his first ever scar, and then the fight was interrupted. Even if it's clear that Oden is not on the same level as the aforementioned pirates, he still managed to leave this much of an impression on Kaido through the damage he was able to inflict in their one fight. Even in his prime, Kaido held as much respect for Oden's strength as he did back when they fought, and we know Kaido doesn't respect Oden as a person.
Oden's final stand
Now just to recap, we know, or can reasonably assume, that some of the things influencing Kaido's respect of these people are

• Reputation: Roger, Whitebeard and Rocks all had insane reputations that surpass Kaido's own
• Fights: Kaido has an on screen fight with Oden where he was scarred and likely fought the other three pirates (at least Roger and Whitebeard) at some point in his life
• Strength: Other than direct fights, we know that Kaido laid witness to all four of these people's strengths personally

And these factors have resulted in Kaido's "top 5" so far consisting of the three strongest pirates to ever do it, and the first man to scar Kaido.
Now we come to the fifth pirate: Shanks. And how is Kaido's relationship with Shanks? We know that Shanks had a billion-berry bounty when he met Luffy and that he became an Emperor 6 years prior to the events of Wano. Shanks was only a kid when Roger died, and during his rise, Kaido had already killed Oden and established his full control of Wano. Kaido left Wano periodically but not for long at a time. The only confirmed meeting that Shanks and Kaido ever had was the one prior to Marineford, which is consistent with the fragile power balance. We are not made aware of any prior or later meetings besides the one in the Marineford arc. Despite this, Kaido still has Shanks in his "top 5."
Is this because of reputation? Unlikely, because, as many are quick to point out, Shanks is not one of the "World's Strongest" title holders. So, unless Shanks is in the list for a separate reason entirely, his placing in that list is almost definitely due to that meeting where Shanks stopped him. But it's also important to note that, by Wano, Kaido was saying he was having the first serious fight of his life in a long time, implying that whatever happened with Shanks that impressed Kaido so much still didn't require Kaido to exert himself, at least not in a one-on-one battle.
This is TCB's translation; I don't have the official on me
This fight was against Luffy. Specifically, a non-Gear 4th, pre-Gear 5th Luffy, who is obviously weaker than Shanks. So it seems that Shanks impressed Kaido without actually fighting him 1 on 1, but it's also clear that Kaido wouldn't respect Shanks if the majority of his strength came from his crew, especially when the lowest standard of comparison here is Oden, who scarred Kaido.
That's actually an important note. Oden scarred Kaido, Shanks didn't. And just giving Kaido a scar on its own isn't enough to be in that list, unless we want to put Zoro up there with Whitebeard. Oden showed parity with Kaido in combat and gave him a relatively massive scar. Yet Shanks, the rival of the World's Strongest Swordsman, gave Kaido no known scar and still got in that elite class of respect.
If Shanks wanted to scar Kaido, he DEFINITELY could have
Everything so far has established the following timeline:

1. The Red Haired Pirates engage Kaido and King in a small-scale battle
2. Kaido is driven away without a scar and without having fought a serious one-on-one duel
3. Two years later, Shanks is put alongside Oden and the Kings

What exactly did Shanks do?
I believe that Shanks did pretty much exactly what he did against Greenbull.
The Haki of Red Haired Shanks
First off, compare the situations. Greenbull was a third party coming into Wano to take on Luffy, and Kaido was a third party going to Marineford to take on Whitebeard. They're definitely similar enough to believe that Shanks reacted the same way.
Second, look at what the technique actually does in Wano. Shanks releases his Haki toward Greenbull, stopping him mid attack and making him exclaim in shock or pain. We then see a sound effect before Greenbull recognizes it as the Red Haired Pirates and Shanks communicates directly with Greenbull from outside of Wano, holding him still the hold time; the Admiral was actually sweating, and eventually he ran away despite having a clear objective.
Now, let's paint a picture of the scene happening before Marineford. Kaido and King are sailing to Marineford when Shanks unleashes his Haki; from what distance, we do not know. Kaido is hit with the Haki and he starts seizing up a bit, stumbling back in his ship, concerned and surprised more than hurt while King starts sweating and shaking. Kaido wonders where the Haki is coming from when Shanks starts communicating with him, telling him something. Perhaps it's a threat, perhaps it's a negotiation around Joy Boy, who knows. The ultimate, relevant point here is that Kaido is getting a first hand taste of the Haki that Shanks possesses, a level of it that surpasses even his own in both raw power and versatility. By the end, Kaido decides to turn back.
This would explain EVERYTHING. Kaido didn't have an actual fight, but there was a conflict that happened where Kaido got to witness Shanks' capability, specifically in the most important of all factors in a fight: Conqueror's Haki. The technique inflicts no injury, so it didn't damage Kaido at all. Depending on the distance that Shanks used it at, it could even explain why he was able to get to Marineford so fast: he was closer to Marineford than he was to Kaido.
I want to be clear that this does not necessarily mean that Kaido was as embarrassed as Greenbull was. Greenbull is a powerhouse as is; if Kaido felt that much Haki coming straight at him, even if it wasn't overwhelming, he'd still be able to easily acknowledge the threat Shanks poses.
But overall, I believe this is the closest explanation for how Shanks dealt with Kaido. If they had a traditional fight, then Shanks would somehow have to impress Kaido without pressuring or scarring him, which could really only mean that he completely dominated Kaido, and I don't think that's consistent. If they had a meeting prior to that where Shanks proved himself, then that only means that a younger version of Shanks than the current one impressed Kaido. And if it's actually based only on reputation, then Shanks must have some insane reputation we are unaware of, which would be consistent with his mysterious Gorosei visits and the respect Sengoku has for him, but even then those aren't necessarily strength related; there's 0 reason for Shanks to be there, but not Mihawk or even Big Mom, based solely on reputation unless there's something we just do not know.

TLDR

Shanks stopped Kaido through Wi-Fi Haki. I believe this because they're only known meeting was prior to Marineford; Kaido was uninjured and didn't have a serious fight, but he still had Shanks in his "top 5." The logical explanation is that Shanks showed off his strength without fighting Kaido, just like he did against Greenbull.
Thanks for reading!

Grabbed this for a deal off FB Marketplace
Doghouse Delta 4 on top of a Kia EV6. Long term plan is to mount on my utility trailers, love some of the ideas in this sub.
Going to be a great summer!

Not my first plat and certainly not my last. It was fun. I did my impossible run together with my NG+ run on different saves. So I had time to prepare and what not. Did the ammo glitch too to get enough nodes for the weapons I wanted to use. In the end I had more than enough ammo for every weapon I was using and it was a fun ride. Hand Cannon was worth it.
Psn: ShockLitSonDei