Patrick's Dreams have him trying to stop a clever villain and helping people out, and even when he fails, he still manages to work his way out of trouble. Patrick just wants to be helpful and is most likely tired of being called an idiot.
Plankton's dreams involve him running away from (and later chasing) a giant monstrous patty. His worst enemy is the Krusty Krab, so it makes sense that its symbol would be the one antagonizing him. Plankton wants power, but Mr. Krabs (and likely, the Krusty Krab, most likely represented by the Krabby Patty) keeps getting in his way and stealing his potential.
Why do we have to collect Sleepy Seeds to unlock Patrick and Plankton in the final level? Since it's Gary's Dream, the seeds are probably stimulating his mind to remember them more.
