Octopus refers to two of Calvin's alter egos. They each appeared in a weekday strip.
In its first appearance, the octopus was purported to "[terrorize] [a] sleepy waterfront community" by snatching tourists on a beach. This would actually be impossible for any octopus, which would be incapacitated outside of the water. An anology for Calvin really just grabbing his mother.
Here, the octopus was a cartoonlike caricature with an anthropomorphic face and character.
Second appearanceIn its second appearance, the octopus was in its natural element performing regular octopus behavior. Threatened by an unidentified enemy, it released a cloud of ink and escaped, as an analogy to Calvin spraying Susie with pen ink at school.
The octopus was depicted realistically here, with convincing textures and acurate morphology.