Plankton Star looks like Patrick, but is shaped like Plankton. He has Plankton's voice but has Patrick's personality and intelligence.
After trying to be arrive back from the mission of going into the Plan B of going to SpongeBob's brain (since Plankton failed to go into Mr. Krabs' brain, and Karen immediately changed plan), Plankton accidentally flew into Patrick, who so happens to arrive inside the Krusty Krab. Plankton, who at the time was Plankton SquarePants, slowly morphed into Plankton Star.
Afterwards, all the memory from SpongeBob has been erased, and instead, Plankton comes back with no Krabby Patty secret formula to give to Karen.