Is paper wallet the same as cold storage?
I strongly advise you read some comprehensive articles on WWW (Google them using phrases like "bitcoin paper wallet", "bitcoin cold storage", "bitcoin hardware wallet"), they are great source of information. Your question is imposible to answer in a short post and involves some basic concepts that you need to grasp well to be able to safely sail the bitcoin ocean. This is my advice only, you'll do what you like, and to answer your question: a paper wallet, if created correctly (and it is a great IF) is a cold wallet. Not every cold wallet is on paper, though. Not every paper wallet is a secure cold wallet.