Puffy Fluffy is a nudibranch and can transform from an adorable fish into a vicious snake head fish form. In each version he's very different.
Cute fish version
Big Purple eyes
Cute, girly eyelashes
Light blue fins & tail
Pink and puffy lips
Light green body
Pink blushes on both cheeks
One triangular tooth
Doesn't get along with other pets
Long, Slender and sluggy (round) light green body
Long, jagged teeth
Multiple tongues with mouths inside
Light blue giant fins & tail
Tongues tend to be sensitive to pain (As seen when Gary yanks the tongues)
SpongeBob bought him so that Gary would not be lonely while he was at work, but he turned out to be a monster. SpongeBob was ignorant of the situation and failed to notice anything wrong with Puffy Fluffy and blames Gary, even after seeing his monster form, while Gary was wrapped up by its tongues and was about to be eaten. SpongeBob was also about to be eaten but remained oblivious, even after Gary saved him. Puffy Fluffy ran away after Gary tied up its tongues together with a leash then Puffy Fluffy ran away due to Gary tying up Puffy Fluffy and SpongeBob blamed Gary by making Puffy Fluffy run away.
Shower In A Can!
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Nudibranches, which is what Puffy Fluffy is, are actually sea slugs.
His multiple tongues might be a reference to the Graboids from Tremors.
When getting Puffy Fluffy from the gypsy, she says something about it being dangerous. This is possibly a reference to the movie Gremlins, in which a man buys a strange pet from a Chinese shop owner, which refuses to sell it to the man because it is dangerous.
Nudibranches appear as the main antagonists in the online game, "Gary's Revenge."
Puffy Fluffy's monstrous and vicious behavior was actually warned to SpongeBob by the gypsy selling the Nudibranches, but he completely ignored her and took one without even paying.
Due to the vivid resemblance of Puffy Fluffy to mogwai (and gremlins), it was probably midnight or after midnight when he transformed (because of eating). This is the same case as the mogwai from Gremlins.