What is the difference between a paper and an e-petition?

There is no theoretical difference, only the way in which the signatures are collected and delivered. A petition can gather names and addresses in either or both forms, though once someone has signed a petition in one format, they cannot sign it in another. Some people may consider e-petitions more convenient as they can then gather 'signatures' via e-mail rather than having to gain signatures in person and the e-petition is submitted online instead of being posted. E-petitions have the added benefit of being published online for a wider audience to view.