Pikmin 4 is a rescue game first. The main objective is not to defeat things - it is to find and rescue 50 castaways scattered across PNF-404, and then track down Olimar. Every castaway has a name, a home planet shown on an ID badge, and a small piece of the story.
Olimar returns to PNF-404 aboard the S.S. Dolphin. A freak accident scatters the ship. He befriends a dog-like creature he names Moss, recovers the ship's Interstellar Radio, broadcasts an SOS along with his Voyage Logs, and then vanishes. Moss stows away, falls ill and grows a leaf on her tail. Olimar crash-lands again, his life support fails, and the Pikmin carry him to an Onion - which turns him into a leafling with almost no memory left. That is the mystery the game is built on.
A leaf-covered alien begins turning castaways into leaflings and challenges you to Dandori Battles. Doctor Yonny and the Lumiknoll Glow Sap reverse the condition. Olimar is rescued and cured, but he returns to PNF-404 when Oatchi begins to sicken the way Moss did - confirming that leaf-bearing organisms cannot survive away from this planet. Oatchi is cured using the Ancient Sirehound's collar, the "Gift of Friendship", during post-game content. Moss does not recover, and Olimar leaves her behind; the Pikmin follow Moss as their new leader. There is a normal ending, a true ending that requires all the ship parts and a final boss, and a secret post-game ending.
Alph, Brittany and Charlie do not appear in Pikmin 4. Three look-alike characters take their place: Yorke, Nelle and Don Bergman, Koppaites who came to PNF-404 hunting treasure to save their own planet from a food crisis. Nelle is a veterinarian. Louie - Pikmin 3's vice-captain - returns as the second-half antagonist, riding the Ancient Sirehound; he and Frankie crash their D.D. Shark on the planet. Olimar's Mechanical Harp plays the Pikmin 3 theme, hinting that Pikmin 3 takes place after Pikmin 4 in-universe. The chronology is deliberately ambiguous and does not fit neatly into the previous three games, so treat "Pikmin 4 is a prequel to Pikmin 3" as plausible but unconfirmed.
Among the named rescues are Schnauz, Dalmo, Corgwin, Jin and Puddle. Their ID badges reveal a wide spread of home planets - Karut, Giya, Ohri, Nijo, Koppai, Hocotate, Siguray, Sozor, Ooji, Flukuey, Enohay, Conohan, Enohee, Neechki, Koodgio, Ogura, Moyama, Mihama, Ocobo, Tagwa and Maxima - which is a small, satisfying detail for anyone collecting every badge.