“Wallet” is a misleading name that unfortunately caught on, for what bitcoin private key managers are. A much more intuitive way to think about it is a keyring. Just like you can copy a physical key, you can also copy a cryptographic key. This is unlike a “wallet”, which holds the currency in it.
There are many ways to generate a key. For a paper wallet, the advantage is that you generated it yourself offline, so you can be confident (if you’ve verified that the generating code is safe) that nobody else has access to your keys; they were never online.
Since new users may see this question, I should note a common pitfall of paper wallets; the way bitcoin transactions work means that spending any less than the total balance of the paper wallet is dangerous when you haven’t prepared for the way the rest of the balance is handled. Make sure you spend the entire balance when spending from a paper wallet.
