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King Neptune first appears in the episode "Neptune's Spatula," where he appears after SpongeBob pulls the Golden Spatula from the ancient grease, making him Neptune's royal fry cook. However, Neptune refuses to accept such a lowly creature as SpongeBob as the chosen one, and challenges him to a cook-off where, if SpongeBob wins, he will become a god in Atlantis, but if he loses, he must give up fry cooking forever. The challenge is held at the "Poseidome", where the first one to make 1,000 patties wins. Using his godlike powers, Neptune wins the challenge just as SpongeBob finishes his first patty. To celebrate his victory, he gives the patties to the audience, who hate it. Neptune then tastes SpongeBob's patty, and loves it. He declares SpongeBob the winner and makes him a god. However, when SpongeBob learns that his friends can't join him in Atlantis, he does not want to go, and instead makes Neptune his "trainee" at the Krusty Krab. In this episode, Neptune is green, and has fairly realistic human features, has hair, a mustache, a beard, thick fingers, is very muscular, and has a different crown. This version of Neptune also appears in Battle for Bikini Bottom, where he summons SpongeBob and Patrick to the Poseidome to defeat a robot version of Sandy.
Neptune plays a central part in The SpongeBob SquarePants Movie. The movie also introduces Neptune's daughter, Princess Mindy. This version of Neptune is green-skinned and far more cartoony than the version in "Neptune's Spatula." He is also explicitly portrayed as a king rather than a god, and lives in a palace just outside of Bikini Bottom rather than Atlantis. This Neptune is very brutish and tyrannical, which he tells his daughter is necessary for him to be respected as a ruler. His crown is very important to him, not only because it is a symbol of his power, but because it covers his "thinning" (bald) head. When the crown is stolen by PlanktonNeptune attempts to execute Mr. Krabs, who is framed for the crime. In "SpongeHenge," Shubie denies Neptune's existence when an anchovy tells her that Neptune must be mad, saying, "Everyone knows Poseidon is the ruler of the undersea."
A picture of King Neptune, as seen in "Neptune's Spatula," is shown in "Krusty Towers." Squidward refers to this Neptune as "Neptune XIV", suggesting that there are multiple King Neptunes, and possibly explaining his inconsistent appearance.
Judging by his different appearances, it is reasonable conclude that Neptune is actually two different characters, with the first one referring to the Roman deity of the same name, and the second one works as the actual King of SpongeBob's underwater world. Their different places of living and the fact that he doesn't know SpongeBob and Princess Mindy only being in the movie reinforces this theory.
Another possible explanation is that he has gotten older from the show to the movie resulting in his loss of hair, because Stephen Hillenburg did establish that the movie does take place after the series.