Shin Shoryuken / Shinku Hadoken
They are named Shin Shoryuken (真・昇龍拳, True Rising Dragon Fist), a three-hit trapping combo, and Shinku Hadoken (真空波動拳, Vacuum Surge Fist), a projectile. Which attack he uses depends on how close he is to an opponent.
When there are no opponents directly in front of Ryu, he will perform the Shinku Hadoken (真空波動拳, Vacuum Surge Fist), a powerful version of his neutral special, Hadoken.
Upon use, the camera zooms in on Ryu while he gathers great amounts of blue energy (Ki) into his hands. He then announces "Shinku... HADOKEN!!", before firing a large blue projectile. Despite the projectile's small size (being only somewhat bigger than an Input Hadoken), it has a strong vacuum effect, which pulls opponents towards it and makes the move deceptively difficult to escape from. Opponents trapped in the projectile take constant damage, and are sent flying when the projectile explodes after traveling the distance of Final Destination.
Shinku Hadoken deals a maximum of 29-30% damage (19 repeated hits for 19%, final hit dealing 10% and carrying all the knockback), assuming the opponent is trapped the moment Ryu unleashes the projectile. The final hit's knockback is somewhat lacking for a Final Smash, only KOing at 115%; it is therefore more efficient to take advantage of the projectile's vacuum effect to drag opponents towards the blast lines, where it can KO much earlier. Finally, the attack overall has little end-lag compared to most Final Smashes, allowing Ryu to quickly get into position to finish opponents who survived the attack.
If Ryu uses his Final Smash right next to an opponent, he will instead perform the Shin Shoryuken (真・昇龍拳, True Rising Dragon Fist), a powerful 3-hit version of his up special, Shoryuken. It has extremely high KO power, but requires precise positioning and typically focuses on a single target.
Upon use, the camera zooms in, and Ryu stuns the opponent with a flash of purple lightning that cuts across the screen (dealing 1% damage), before swinging his right fist for an uppercut (10%). He then performs another uppercut with his left fist, briefly pausing mid-uppercut against the opponent's chin while grunting the word "Shin..." (10%), before leaping upward and announcing "SHORYUKEN!!" (20%). The first two punches cause white ink-like effects, while the final blow causes black ink to surround the opponent while violent action lines focus on the Final Smash's victim.
The move deals 41% damage in total, and the final hit is extremely powerful, enough to KO reliably at 28%, although Ryu has to be close (sometimes even touching) the opponent for it to activate, otherwise his Final Smash becomes the Shinku Hadoken. The Final Smash can miss at this range as well, either due to intangibility, or being too far away to be trapped; if so, Ryu performs a 6-hit Shoryuken, dealing only 15% damage, before landing on the ground.
There is a unique aesthetic effect of the final blow if the opponent is dealt enough knockback to be KOed: the entire screen becomes covered in an orange background, along with a unique sound effect and Ryu announcing "SHORYUKEN!" in a fiercer tone. This background and sound effect are used in the Street Fighter series when a fighter is KO'd by a Super or Ultra Combo. The background does not appear if the last hit does not have enough force to KO the opponent (e.g. if the opponent is at 0%).
Use this attack when Ryu is far away from an enemy to unleash a Shinku Hadoken that penetrates through the stage. But if you use it when Ryu is close to an enemy, he’ll unleash a Shin Shoryuken uppercut attack. When it hits, Ryu will follow up with his other fist and launch the opponent up, up, and away!
Ryu's Final Smash takes on two different forms depending on how close Ryu is to the enemy. If he's farther away, he'll use Shinku Hadoken, a move that pulls in any enemies nearby. If closer, he'll instead use Shin Shoryuken. He'll hit the enemy once with a powerful uppercut, then follow it up with the other fist to finish the job!
Note that the trophy only depicts Shin Shoryuken.
The Shinku Hadoken first appeared in Super Street Fighter II Turbo as his trademark Super Combo (its name wasn't originally presented onscreen until Street Fighter Alpha) that later appeared in several games ever since its debut. In most Street Fighter games, it is a somewhat-larger, a multi-hitting version of the Hadoken which paved way for projectile durability ratings in other fighting games (when different projectiles clash with each other to see which one comes out on top).
In most of the Vs. Capcom crossovers, it instead becomes more akin to a laser beam akin to the Kamehameha technique from the Dragon Ball franchise. In-universe, it is a Hadoken coated with vacuum energy to increase its damage and size, hence the literal translation of the technique's kanji. In those games, Ryu is able to perform both his normal Hadoken and Shinku Hadoken in the air.
The Shin Shoryuken was introduced in Street Fighter III: New Generation as Ryu's second Super Art, which also appeared in several games since its debut. As such, the Street Fighter III series version of his final smash is the one the Smash version is based off of. This move was first taught by his master Gouken. The version seen in Smash combines the effects of both the first two hits of Gouken's Shin Shoryuken with the final hit effect of Ryu's Metsu Shoryuken. In some games, Ryu would perform a spiraling turn true to Shoryuken-fashion at the peak of his rise (in most old Vs. Capcom series games), while in the attack's standalone debut in Street Fighter III and in recent titles he and Gouken omit the classic peak-turning motion.
In Street Fighter Alpha 3 (or Zero 3 in Japan), Ryu would be able to perform the Shin Shoryuken out of his Metsu Shoryuken Super Combo only if he hits with the very final frame of his initial elbow lunge (practically out in the open, it requires very proper and specific spacing). Otherwise, Ryu will perform a normal Shoryuken as the finisher.
The screen that shows up in the background on the final strike of Shin Shoryuken is the KO screen from the Street Fighter IV games, which would show up whenever the opponent lost all their health at the end of a round if attacked by a Super/Ultra Combo.
Finally, the fact that Ryu has two Final Smashes is a reference to the Ultra Combo Double mechanic introduced in Ultra Street Fighter IV where the player, instead of sticking with one Ultra Combo or the other, can use both at the cost of reduced damage on each one. In Ryu's case this would be the Metsu Hadouken and the Metsu Shoryuken.
It may also be a reference to how in Street Fighter IV, some Ultra Combos would change if they missed or were blocked. Some examples are Ken's Shinryuken becoming a simple flaming uppercut if it misses (making it akin to the original Shinryuken prior to Street Fighter IV) or Oni's Tenchi Sokaigen being a shockwave instead of a cinematic uppercut should the opponent block it. Ryu's Shin Shoryuken in the Street Fighter III series, Marvel vs. Capcom 3, and his Metsu Shoryuken in Street Fighter IV all also share this property, becoming simply stronger and/or multi-hit Shoryukens if they miss or are blocked (as well as being spaced properly so the initial Shoryuken connects in a way to not trigger the actual attack). Ryu's Shin Shoryuken in Super Smash Bros. retains this as well.