There is only one glorious and powerful King Neptune in SpongeBob SquarePants, his character designs are just different in Neptune's Spatula/SpongeBob VS. The Patty Gadget (which are regular SpongeBob episodes) and The SpongeBob SquarePants Movie (which was a movie that hit the movie theaters.)
If Neptune's Party is going to be a regular episode or Special, then I think the Neptune character design is very likely going to be the ones from Neptune's Spatula and SPongeBob VS. The Patty Gadget. (If you didn't notice, there is a short scene showing Neptune in that episode after SpongeBob defeats the gadget, after Patchy's quote "The blast is was so loud, it woke King Neptune!") And his character design in that episode looked like it was the same one in Neptune's Spatula.
Wow, I can't wait to see this cool new episode showing King Neptune again after so long! If you count the movie, this episode is only going to be King Neptune's fourth appearance out of the entire series, King Neptune is a very rare and valuable character to be seen in this show indeed.