Sure, Peter is a comic character. But keep in mind that the comic version could have more complex plotlines and interactions with other characters that might not have been fully explored in the movie.
Peter could be any number of things. Maybe he's a unique creature that doesn't exist in the real world, like a talking animal with superpowers. Or he could be a regular animal that Deadpool just decides to name Peter and make into his pet.
Peter would probably be shocked at first. I mean, getting a call from Deadpool in the middle of class is not an everyday occurrence. He might quickly look around to see if anyone noticed his phone ringing.
One common theme is the clash of personalities. Peter is more of a by - the - book hero with a strong moral code, while Deadpool is chaotic and often breaks the rules. Their interactions based on these differences are often explored.